Narrative Project Description

Princeton and UTokyo Educational Partnership in Interrelationship of Plasma Sciences in Laboratory and in Space Stewart Prager (PI) and Masaaki Yamada (Co-PI), Princeton Plasma Physics Laboratory, Princeton University Yasushi Ono (PI), Graduate School of Frontier Sciences, University of Tokyo

I. Introduction and Scope of Proposed Program The University of Tokyo (Departments of Advanced Energy, Complexity Science and Physics, Electrical and Electronic Engineering, Aeronautics and Astronautics and Earth and Planetary Physics) and Princeton University (the Princeton Plasma Physics Laboratory, PPPL, Department of Astrophysical Sciences) propose to establish a next stage of the educational partnership that provides undergraduate and graduate students experiences in the related areas plasma sciences in the laboratory and in space. The scientific focus is interdisciplinary in three ways. First, within the field of plasma physics it is aimed at physics and engineering that apply to laboratory plasma experiments, to plasmas in space (in the solar system or heliosphere) and to plasmas studied for fusion energy and plasma rocket applications. Second, the program will provide students international joint lectures and practices in experiment, theory, and observation. This interdisciplinary application of plasma physics and engineering is a growing area of science, as the techniques and insights developed separately by the solar/space/astrophysical plasma community and laboratory fusion plasma community are shared with fast pace. This increasing interaction between the three or four communities is accelerating in both disciplines. Exposure of students to the research problems, common sciences, and experimental, observational and theoretical tools of both communities will provide educational experiences well beyond that received in the classroom. In particular this program will provide a platform for international exchanges of undergraduate students who have aspirations for pursuing a career in the global research environment.

1 The proposed educational program builds on a long and productive collaboration between senior researchers at the University of Tokyo and Princeton University. A long-standing collaboration has involved joint research on basic plasma experiments at both Tokyo and Princeton. This work has involved visits of senior scientists that have interacted with graduate students on-site. The earlier emphasis has been nearly entirely on senior researcher collaboration, with no organized training or exchange of graduate students, and no participation of undergraduates. This set the stage for the new partnership that was initiated three years ago.

The past three years of the Tokyo/Princeton partnership in plasma physics has established a dynamic, popular interdisciplinary educational program for undergraduates and graduate students. We have set up a summer school, a lecture series and, most importantly, a well-directed exchange program for student research in areas at the forefront of plasma physics. Students, both undergraduate and graduate, report that the experience has been enormously rewarding, both scientifically and culturally. We propose to extend the program, upgraded with improvements, for another three years. This will build on the substantial investment of effort that was expended to set up the new program so that a new generation of students can reap the educational returns of that effort. The proposed program has three components: A plasma summer school for undergraduate and beginning graduate students: Each summer we will have a 7 – 8 week summer school for undergraduate and graduate students. The school will begin with 1 – 1.5 weeks of classes in interdisciplinary plasma physics. It will be followed by 6 – 7 weeks of research training for undergraduates at the site of the school, which will alternate between Princeton and Tokyo. The school will also include weekly seminars for students to share research progress and cultural perspectives. We anticipate about 6-8 undergraduate participating each summer (3-4 from Tokyo, 3-4 from Princeton) and about 4 graduate students (2 from each side).

Lecture series and workshops:

2 For a three-month period, possibly in part overlapping with the summer school, we will organize weekly lectures for the students by senior researchers. The lectures will be video broadcast to encompass students and researchers at both universities followed by Q&A sessions using internet (Zoom) connection. These lectures will be coupled with the on-going graduate courses “Advanced Plasma Physics and Engineering” for graduate students and “Plasma Physics and Engineering” for undergraduate students of the University of Tokyo. Annually, a research workshop will be held, with participation of senior researchers and students, to discuss new research results and directions. In collaboration with this proposed program, the graduate course seeks a special support from “Prominent Graduate School”「卓越大学院」of the University of Tokyo.

Joint research by exchanging graduate students: Graduate students will participate in our joint research, relevant to their Ph.D. thesis research, in the partner university. We anticipate that the exchanges will involve about 1- 2 students annually from each institution, depending on availability or research opportunity. Particularly in 2018, a joint group research for exchanged students is planned to be supervised by senior physicists on the new FLARE (Facility for LAboratory Reconnection Experiment) device which is expected to be completed in Princeton in 2017. In 2019, a similar type of joint experimental research will be carried out on TS-U, which will be completed also in 2017 in Tokyo. Below we describe the scientific area of the collaboration (Section II), past research collaboration as a foundation for the educational program (Section III), further details of the three components of the proposal (Section IV), the responsible staff members (Section V) and a budget explanation (Section VI).

II Plasmas in the Laboratory and Space

Plasmas, ionized gas– in which electrons are stripped away from the nuclei- are complex states of matter that exhibit a huge array of phenomena that challenge our ability to describe and understand collective behavior. Plasma physics has been particularly driven by two grand challenges. The first is to develop fusion energy as an energy source to

3 transform the way the world produces energy. This requires producing, controlling – and understanding – a plasma at a temperature of 100 million degrees confined by a magnetic field. The sun produces its energy by fusion; the goal to produce fusion energy on Earth for electricity generation is often aptly described as producing a sun in a container. The second challenge is to understand the behavior of natural plasmas in the universe. The majority of matter in the visible universe is in the plasma state. Behavior of the solar system is significantly determined by plasma physics. The Earth is embedded within a plasma (the ionosphere and magnetosphere), the solar wind transports plasma from the sun to the Earth, and the Sun is a plasma. Moreover, plasmas are key to behavior at all scales in the universe – from the plasma filling the interstellar medium to extra-galactic jets of plasma that emanate from disks surrounding black holes.

The past decade has seen a growing interaction between the two communities – that of laboratory plasma physics and plasma astrophysics. Remarkably, there is an enormous amount of physics that is shared between phenomena in the laboratory and in the cosmos. Experiments cannot nearly reproduce the conditions that exist in astronomical plasmas, but they are invaluable in isolating and studying physics processes that underlie astronomical plasma behavior. In addition, theoretical and computational tools are transferable between the two communities. The growing interaction between the two communities is boosting progress in both, leading to new collaborations and new insights.

The proposed educational program will introduce students to the common physics of laboratory and astronomical plasmas, as well as the leading edge challenges. They will be taught by leading practitioners at the interface between laboratory and astrophysical plasmas, and will participate in research, both experimental and theoretical. To contain the breadth of the program somewhat, the focus on astronomical plasmas will be mostly limited to plasmas within the solar system. This involves the plasma physics of the sun, the solar wind, and the Earth’s plasma sphere (although the basic phenomena studied are also highly relevant to plasmas far beyond the solar system). A phenomenon of particular importance is magnetic reconnection – a process in which magnetic field lines tear and reconnect. In so doing, the magnetic topology within the plasma is drastically altered,

4 with huge effects on the plasma embedded in the magnetic field. Magnetic reconnection underlies phenomena from geomagnetic storms to solar flares to disruptive events in laboratory fusion plasmas.

III Past educational and research collaborations

For roughly 30 years, there have been research collaborations underway between PPPL and the University of Tokyo. These have focused on the area of magnetic reconnection, particularly through joint experiments in the basic reconnection experiment at PPPL (the Magnetic Reconnection Experiment, MRX) and a similar experiment at the University of Tokyo (the TS-3/4 experiment). The collaboration has consisted of exchange visits of research scientists, joint experiments, and comparative studies of results from the two experiments. In addition, we have worked together to organize research workshops, such as the annual US-Japan Workshop on Magnetic Reconnection and the bi-annual international meeting IPELS (Interrelationship of Plasma Experiments in Laboratory and Space). These collaborations are not focused on education, but on research with the major participants being senior researchers. Since 2015, we have developed a new form of collaboration, the educational partnership program of plasma physics, with a focus on fusion energy and solar observations; See Appendix-1, a slide summary of our program. We formulated and established mutual exchange of students (undergraduate and graduate) and researchers, exploiting the strong synergies between the two complementary experimental facilities.

Achievement of the previous period We established a very successful joint summer school of interdisciplinary plasma physics for about 20 students at Princeton University in 2015 and at the University of Tokyo in 2016. As of February 1, 2017, we have exchanged 10 undergraduate students and 5 graduate students for 1.5 week-long school sessions followed by joint plasma experiments, solar observation and theory/ simulations. In FY 2015, 4 undergraduate students from the Department of Physics in Princeton University and 3 undergraduate

5 students from the University Tokyo participated in the program. After they attended a week-long plasma physics course together with the Summer Undergraduate Research Internship Program at PPPL, they listened to the lectures of experts from Princeton - Prof. A. Bhattcharjee, Dr. M. Yamada, Prof. H. Ji, and Dr. M. Ono and from Tokyo - Prof. Y. Ono and Prof. Hoshino. In FY 2016, a week-long plasma physics course was taught by similar members at the University of Tokyo and an almost equal number of student exchange were made between Princeton and Tokyo. As of Feb 10 th of 2017, we are expecting many applicants for our FY2017 program as seen in Appendix II.

Our summer school is the first and best opportunity for most students of University of Tokyo to learn the interdisciplinary plasma physics. They learned for the first time the close relationship between fusion plasma experiments and the magnetospheric phenomena. This experience helped them to develop their own ideas which interrelate experiments, observation and simulations. Prof. Ono’s group recently received a preparatory budget for “Prominent Graduate School” and they hosted the first Spring School and Workshop for magnetic reconnection phenomena in space and in laboratory in Napa CA, USA (March, 2016) and the second Spring School and Workshop in Matsuyama. Japan (March 2017). The spring school had 5 tutorial talks for initial trial for education and research for about 10 participating graduate students in 2016.

6 Our program of joint lectureship and student exchange has become so popular among participating students that many students have been reapplying to this program. One Princeton student said, “I met and learned from many wonderful Japanese scientists who taught me many things about physics and Japanese cultures. I've come to really appreciate Japanese work ethics, cultural values, and am very motivated to continue studying plasma physics.” Another Princeton student stated, “I am humbled by both the beauty of Japan and the hospitality of its people.” More detailed student reports for FY 2015 and 2016 can be found in the Appendix IIIA and IIIB.

Joint Lecture in University of Tokyo Excursion to Nikko National Park

IV Proposed Activities With a commencement of the newly built scientific user-facility at Princeton, FLARE, we here propose a new phase of the educational cooperation and partnership. The plasma summer school: Each summer will include a 7 – 8 week summer school for undergraduate and beginning graduate students. The school will begin with 1 – 1.5 weeks of classes in interdisciplinary plasma physics. In every other summer at PPPL, the classes are merged with an ongoing program for US undergraduates – the Summer Undergraduate Research Internship program, funded by the Department of Energy. This long-standing program starts with an intensive one-week school with lectures given by plasma physicists from across the US. This one-week experience has been documented to be extremely successful with large impact on the future paths of the students. The students of the Tokyo/Princeton program will partake in this lecture series and then receive additional lectures essential for our proposed program after it.

7 Student research The school will be followed by 6 – 7 weeks of research training for undergraduates at the site of the school. At PPPL, students can work on magnetic reconnection in the ongoing facility, MRX, and in the newly constructed user-facility, FLARE. Also available as part of the program is a major fusion device (the National Spherical Torus Experiment- Upgrade, NSTX-U), and a plasma thruster research device at PPPL. At the University of Tokyo students can work on the basic experiment in magnetic reconnection, TS-4 and on a fusion toroidal confinement facility (the University of Tokyo Spherical Tokamak, UTST), which shares physics in common with the NSTX-U facility at PPPL. The experiments are located at the Kashiwa and Hongo campuses. Students can also participate in analysis of data from the Hinode solar satellite which is operated under the auspices of the University of Tokyo. Also data from MMS (Magnetospheric MultiScale Mission) which was launched in 2015, will be utilized for research of magnetic reconnection in space. The Hinode, launched in 2006, is a Japanese solar satellite equipped with three advanced solar telescopes: the optical telescope (SOT), the X-ray telescope (XRT) and the EUV imaging spectrometer (EIS). These telescopes will reveal the heating mechanism, the dynamics of active solar coronae as well as magnetic reconnection phenomena. The summer school students will participate in analysis of data from this satellite and receive research training. The facilities involved in the proposed work are illustrated in Figure 3 including new HTX in Princeton and UT-58 in Tokyo.

NSTX(PPPL) (PPPL) UTST(UTokyo) TS- (UTokyo)

Hinode& HTX& (JAXA#UT) (PPPL)

TST-2(UTokyo) UT#58&(UTokyo)&

8 Fig. 3: Plasma experiments, Hinode satellite and Hall Thrusters at PPPL and the University of Tokyo for research training and collaboration

The school will also include weekly student-run seminars for students to share research progress and cultural perspectives. The dominant interactions between students will occur informally through daily interaction in the classroom and the laboratory. It is important for students to present research results to other students. They will learn physics and other larger issues (on fusion energy, scientific culture in US and Japan etc) through discussions. We anticipate about 6 undergraduate and about 6 graduate students will be involved in this activity each summer .

Lecture series and workshops: For a three-month period, possibly in part overlapping with the summer school, we will organize weekly lectures for the students by senior researchers. Annually, a research workshop will be held, with participation of senior researchers and students, to discuss new research results and directions. The lectures will be interdisciplinary, covering fusion plasmas, space plasmas, laboratory measurement techniques, and numerical simulation techniques. These lectures can be a part of the on-going graduate courses of University of Tokyo: Advanced Plasma Physics, Plasma Diagnostics and Fusion Science Special Lecture, and an undergraduate course: Plasma Physics and Engineering. The lectures will be video broadcast to encompass students and researchers at both universities followed by Q&A sessions using internet (Zoom) connection. Although oriented towards students, the lectures will also be of interest to researchers. Annually, a research workshop will be held, with senior researchers and students, to discuss new research results and collaborations. This will likely include about 15 – 20 participants, and will focus on research projects that involve the students. One option is to have this workshop follow the larger annual US-Japan Workshop on Magnetic Reconnection. Those workshops are quite distinct. The US-Japan Workshop involves many institutions and is focused on research carried out by research scientists. The proposed research workshop for this program is a follow-up gathering of only Princeton and Tokyo students and researchers, focused on our collaboration. Having it co-located

9 with, and following, the US-Japan Workshop could provide an extra scientific opportunity to students by easing their travel logistics and budgets.

Graduate student exchanges: Graduate students will participate in joint research, relevant to their Ph.D. thesis research, in the partner university. This will require careful advance planning such that joint experiments are well-defined, measurement tools are available and functional, and data analysis programs are developed. Projects will be selected that can lead to journal publications and be synergistic with the student’s research at their home institutions.

We are considering the following research related exchanges; 1) Results from the solar flare experiments in MRX at Princeton will be compared with solar observations from Hinode at Tokyo. An exchange of graduate students can be made between the two research groups. 2) A particle acceleration theory of Prof. Hoshino's group in Tokyo will be tested in MRX at Princeton; 3) Current drive and plasma startup schemes tested by Prof. Takase's group at Tokyo can be applied to NSTX-U in Princeton, and 4) Fusion stability simulation done by Dr. Elena Belova's group at Princeton can be applied to stability experiments by Prof. Ono's group in Tokyo. We anticipate that the exchanges will involve about 3 students annually (2 from Tokyo, 1 from Princeton).

V. Participating Staff The proposed program will be executed by a committed group of senior researchers from each institution. The PPPL staff includes Prof. Stewart Prager, Dr. Masaaki Yamada, Prof. Hantao Ji, Prof. Amitava Bhattacharjee, Dr. Masa Ono, and Dr. Yevgeny Raitses. Prof. Prager will function as the principal investigator, drawing on earlier experience directing an interdisciplinary, multi-institutional NSF center – the Center for Magnetic Self- Organization in Laboratory and Astrophysical Plasmas – that spanned topics similar to those of the current proposal. The proposed work builds upon a long-standing collaboration between Dr. Yamada and Prof. Yasushi Ono, the principal investigator from the University of Tokyo. Dr. Yamada, the originator of the Magnetic Reconnection

10 Experiment also functioning as a Co-PI and Prof. Ono will assume responsibility for the execution of the proposed work. They will draw upon their combined experience in prior Princeton-Tokyo research collaborations. Prof. Ji, an experimentalist heading FLARE facility and Prof. Bhattacharjee is a theorist, both with deep experience in magnetic reconnection and all physics topics contained within the proposal. Dr. M. Ono is heading the collaboration effort of NSTX-U facility and an expert in tokamak confinement physics. All US staff members have extensive experience collaborating in Japan, and in many cases living in Japan. Dr. Raitses is the head of the research group on plasma propulsion. (See Appendix IVA) The University of Tokyo staff consists of Prof. Y. Ono in Department of Advanced Energy/ Electrical Engineering, Prof. Takase in Department of Complexity Sciences/ Physics, Prof. Hoshino and Prof. Yokoyama in Department of Earth and Planetary Physics and Prof. Inomoto in Department of Complexity Sciences/ Electrical Engineering. Prof. Y. Ono, the Univ. Tokyo-side principal investigator, directs an interdisciplinary center for magnetic self-organization and reconnection for Japan. Prof. Y. Ono is the project head of the TS-4 and an expert of tokamak merging / reconnection experiment. Prof. Takase and Prof. Inomoto are the project head of TST and UTST, respectively and are the experts of spherical tokamak experiments. Prof. Hoshino is a space physicist and theorist with deep experience in magnetic reconnection and self-organization and Prof. Yokoyama is a solar physicist analyzing the magnetic reconnection measured by the solar satellite Hinode. Prof. Komurasaki is a rocket engineer who has been developing his Hall plasma thruster in his device UT-58. Prof. Koizumi has been developing the plasma thruster for the future long distance trip of satellite. All Japanese staff members have extensive experience collaborating in US, and also living in Princeton (See Appendix IVB).

VI. Budget Explanation

We are planning about a 42 person-month exchange, with requested funds covering travel expenses (36 for students and 6 for faculty and research staff) as shown in “Breakdown of

11 funds requested.” FTE charges are covered by the home research funds and not included in this request or the attached table. The partnership is facilitated by significant internal funding provided through other channels. The Faculty of Frontier Sciences of University of Tokyo allows us to use the visiting professor position for leadership positions of the proposed plasma school and exchanges. Additionally, the University of Tokyo will also use the internal faculty supporting fund to support the proposed plasma schools: UTSIP (University of Tokyo Summer Internship Program), UTRIP (University of Tokyo Research Internship Program) and another one for interdisciplinary collaboration; the Science Fusion budget to host the plasma schools and workshops at Tokyo. Finally, the Tokyo-side will utilize the exchange programs GSP (Global Summer Program) to send U. Tokyo students to Princeton University. For long-term sustainability of the new program, we will also try to receive several international collaboration budgets from the Japan Society for the Promotion of Science (JSPS). Finally, we are now proposing to upgrade our Princeton- UTokyo plasma education program to one course of “Prominent Graduate School” or 「卓越大学院」scheduled in 2018 by Ministry of Science and Education. Our proposal already ranked second in the Graduate School of Frontier Sciences are now waiting for the final decision by UTokyo. In Princeton, research funding from NSF and DOE underlies the program through support of senior researchers, graduate student stipends, and experimental facilities. Such support derives particularly from the Princeton participation in the theory department and FLARE-MRX facilities. In addition, we will request supporting funds from Friends of UTokyo (FUTI), US-based association for University of Tokyo alumni, in order to facilitate the student exchange. All of the funding sources mentioned above are expected to be long-term, able to support the proposed Princeton-Tokyo plasma education collaboration beyond this proposal period. Especially, the visiting scholars in both universities are expected to be a core for the proposed collaboration.

12

Laboratory observational & theoretical researches have advantages and disadvantages Interdisciplinary research

PU-UT J-Education Reports presented by 45 UTokyo Students Kazutake Kadowaki: Dept. Electrical Eng.) Kota Hirabayashi: Dept. Earth & Planetary Science) Adviser: M. Yamada (PPPL) Adviser: J. M. Stone (Dept. Astronomy)

Report on Collaborative Research at Princeton Reports presented by 45 UTokyo Students Kazutake Kadowaki: Dept. Electrical Eng.) Kota Hirabayashi: Dept. Earth & Planetary Science) Adviser: M. Yamada (PPPL) Adviser: J. M. Stone (Dept. Astronomy) Mr. Kadowaki (by M Yamada) experimentally tested asymmetric reconnected magnetic field in MRX pull-mode reconnection.

Asymmetric in-plane magnetic field

2cm 5cm 5cm 5cm

Internal coil 2D magnetic field probe array region

Reconnected field = Br [T]

0.8mT/cm 2.0mT/cm

Magnetic Reconnection Experiment (MRX) We clearly observed asymmetric energy outflow in agreement with space observations

Measured range of Langmuir probe (ne, Te) scanning Mach probe (Vi) IDSP (Ti)

Probes on MRX wall

Right Left Caliculated energy fluxes in each outflows Reports presented by 5 UTokyo Students Kento Nishida: (Dept. Advanced Energy) Adviser: M. Ono (PPPL) Tomohiro Hamada: (Dept. Electrical Eng.) Adviser: H. Ji (Dept. Astronomy, PPPL)

Yusuke Yoshida: (Dept. Complexity Sciences) Adviser: J. Menard (PPPL) Feb.25 – Mar. 30

Opportunities for Summer Research in 2017: The Princeton-UTokyo Partnership on Plasma Physics

Princeton Plasma Physics Laboratory, Princeton University Graduate School for Frontier Sciences, U. Tokyo Two of the world’s leading centers for plasma research — the Princeton Plasma Physics Laboratory (PPPL), Princeton University and the University of Tokyo — have joined forces in a new initiative: an exchange program in plasma physics for undergraduate and graduate students from both institutions. Taught by faculty members who are pioneers in plasma physics for fusion and space plasma physics, the program will introduce students to the research problems, common physics, and experimental, numerical and theoretical tools of both areas of study. The U. Tokyo/Princeton Educational Partnership in Plasma Physics will expand the educational horizons and global research opportunities of their undergraduate and graduate students. FY 2017 Plans [1] A Summer School on Plasma physics (1.0+ week) scheduled in June, will be held at PPPL. A part of the program will be carried out jointly with the DOE Summer Undergraduate Research Internship Program. Both undergraduate students and beginning graduate students participate from each university. [2] Students internship and training during the following 5 weeks after the summer school. [3] Long term research exchanges (Grad student/post-doc)

Student research can involve fusion and astrophysics experiments at PPPL and U.Tokyo and data analysis from the Hinode satellite.

Core components of the exchange program are a “plasma summer school” with research training and classes for interdisciplinary plasma physics for both undergraduate and beginning graduate students, a weekly lecture series and workshop with prominent researchers, and graduate student exchanges which include joint projects leading to doctoral research. Students will be directly involved in research that is advancing the frontiers of both fusion and space plasma physics. At Princeton, students can participate in an experiment on magnetic reconnection, in laboratory astrophysics and exploratory fusion experiments. At the University of Tokyo, students can work on a toroidal plasma merging experiment for magnetic reconnection in advanced fusion research and on data from the space satellites including Hinode.

Application should be sent to Dr. Masaaki Yamada E Mail: [email protected] Princeton-UTokyo Educational Plasma Partnership Program: PPPL, Princeton University

Deadline: February 15, 2017

Application material: 1-2 page letter which describes student’s background and reasons for application At least one recommendation letter; CV of applicant which includes GPA.

One Dimensional Electrostatic Particle in Cell Simulation of Plasma Instabilities

Horace Zhang with Professor Masahiro Hoshino

August 27, 2015

Abstract Using one dimensional particle in cell simulation code, we investigate the two stream and Buneman instabilities in a charge neutral and cold plasma subject to periodic bound- ary conditions. The growth rates of the electric field wavenumber modes are compared to those theoretically predicted by the dispersion relation of the two instabilites. Computa- tional growth rates show excellent agreement with theoretical predictions. These results demonstrate that 1D-Particle in Cell (PIC) methods provide an accurate way to model the theoretical behavior of plasma in this regime.

1 Particle in Cell Method

In a PIC simulation, one uses a continuous range of particle positions and velocities. However, the field quantities (ρ, V , E), (charge density, electrostatic potential, electric field) have discrete values linearly spaced across the system size. To interpolate from particle positions to field quantities and vice versa, shape functions are used. We choose a linear interpolation method where each particle contributes to its two nearest grid points as the shape function. In this way, particles are trapped within the grid “cells”. The PIC simulation method is as follows:

1 Initialize electron and ion positions (xi) and velocities (vi) 2 Use shape function to interpolate from particle to grid to find ρ

3 Solve for electric potential via Poisson’s equation on grid 2V = 4πρ ∇ − 4 Find electric field E from potential. E = V −∇ 5 Use shape function to interpolate from grid to particle position

6 Advance particle velocities using dv/dt = qE/m where q is charge and m is mass

7 Advance particle positions using v = dx/dt

8 Repeat steps 2-7

2 Normalization

To simplify calculations, quantities involving position and time are normalized to natural plasma units. Time is normalized to the election plasma frequency ω 1 while position is normalized pe ≡ to the Debye length λD. With these definitions the electron thermal velocity, vth = λDωpe is also unity. From these normalizations appropriate definitions of charge and mass follow. The mass ratio of electrons to ions m m /m is 100 throughout. r ≡ i e

1 3 Simulation results

3.1 Thermal run In a charge neutral plasma consisting of equal numbers of ions and electrons with thermal veloc- ities, Langmuir waves at ωpe and ion acoustic waves are expected. We check for the existence of these waves by comparing the numerically calculated dispersion relation to the theoretical one. The theoretical dispersion relation is found by linearizing Gauss’ Law, the particle equation of motion, and the continuity equation. From the Fourier transform of the simulated electric field profile, E(t, x) Eˆ(ω, k), the plot of the power-spectral density Eˆ(ω, k) 2 vs (ω, k) in a heat → | | map is shown in Figure (1). Energy conservation and charge neutrality are checked at each time step. We use a system size of L = 200, a time step of dt = 0.1 for 7,000 steps, (Ng = 201) grid points, and (Np = 20, 000) particles.

Figure 1: Numerically calculated dispersion relation for a thermal charge neutral plasma. The parabolic structure centered at ωpe = 1 is the Langmuir wave. The linear structure is the ion acoustic wave.

3.2 Two Stream Instability The two stream instability consists of two counter streaming electron beams in a background of cold and stationary ions. In this run vth = 0 so the electron drift velocity acts analogous to vth. In this simulation we use L = 500, dt = 0.1 for 3,000 time steps, Ng = 501, Np = 60, 000, and electron beam velocities of 10. Simulation results of electron (v, x) phase space, the spatial ± electric field, and the electron and ion densities are shown in Figures (2) and (3). These simulations show that electron“holes” appear in phase space as the instability is growing. Each electron hole corresponds to a jump in the electric field. To compare the growth rate of the electric field k modes to theoretically predicted ones, the dispersion relation for a cold two stream instability is

ω2 ω2 ω2 1 pi pe pe = 0. (1) − ω2 − 2(ω kv /2)2 − 2(ω + kv /2)2 − d d Here ωpi is the ion plasma frequency and vd is the electron beam velocity. Because the oscillating first order electric field has the form eiωt, the largest imaginary solution for ω in the dispersion

2 Figure 2: Simulation results of electron (v, x) phase space, the spatial electric field, and the electron and ion densities for two times. First column t = 12.0, second column, t= 17.0. relation gives the growth rate for each k mode. The growth rate for each of the k modes is obtained by taking the Fourier transform of E(x) at each time step and tracking the power spectral growth of particular k modes. Figure (4) shows the growth of two different E(k) modes, and the computational and theoretical growth rates for them. The zeroth mode is where k = 0, and subsequent modes (k = 1, 2, 3...) are spaced according to the Nyquist sampling frequency in position space. Generally, equation (1) is solved to give a growth rate γ for each wavenumber k. Figure (5) shows the numerical solution to (1) with the computational growth rate for different wavenum- ber’s overlain. Error bars are one standard deviation from uncertainty in fit parameter. Growth rates are only obtained from k modes where there is a clear period of exponential growth.

3.3 Buneman Instability An additional instability this PIC code can evaluate is the Buneman instability. This instability consists of a single cold electron beam streaming into a background of static cold ions. The

3 Figure 3: Simulation results of electron (v, x) phase space, the spatial electric field, and the electron and ion densities for two times. First column t = 32.0, second column, t= 50.0.

Figure 4: Growth of the k = 6, 7 modes of the electric field for the two stream instability. Computational results and theory agree very well.

4 Figure 5: Solution to the two stream dispersion relation (1) with growth rates obtained computationally overlain. The simulation shows excellent agreement with theory over a range of k modes. Error bars are one standard deviation from uncertainty in fit parameter. dispersion relation is then ω2 ω2 1 pi pe = 0 (2) − ω2 − (ω kv )2 − e where ve is the electron beam velocity ve = 10. All other simulation parameters are identical to the two stream simulation. The numerical solution to this dispersion relation is shown in Figure(6a). This shows that the maximum growth rate of γ 0.135ω is obtained at ∼ pe about k = 0.1. The computational growth of this mode is shown in Figure(6b). Theory and computation again agree well. We find the computational value of γ = 0.134 0.0001ω while ± pe the theoretical growth rate is γ = 0.1357ωpe.

(a) Dispersion relation solution for the Buneman (b) Buneman instability: growth of the theoreti- instability cally predicted fastest growing electric field mode.

Figure 6

4 Conclusion

An 1D electrostatic PIC code is used to analyze a thermal charge neutral plasma, the two stream instability, and the Buneman instability. Our simulation reproduces the Langmuir waves and ion acoustic waves expected for a thermal plasma. For the two stream and Buneman instabilities,

5 the growth rate of the k modes of the Fourier transformed electric field agree very well with the theoretically predicted growth rate. This demonstrates that PIC methods provide an accurate simulation method for modeling plasmas in the regimes tested.

5 Appendix: My Time in Japan

5.1 Research and Work Experience My lab group was very welcoming, and everyone was willing to answer my questions, providing lucid explanations every time. I learned quickly that members of my lab group worked from 9am to 7pm most days, longer than I was initially used to, and certainly much longer than in Germany, where I spent last summer. However, I adapted to this schedule and my work was interesting enough that I didn’t mind staying later. Despite their hardworking nature, the camaraderie among my group members was evident. We ate lunch together everyday and had welcome and farewell banquets. I am grateful to have spent my summer with a diligent and fun loving group of people.

5.2 Travel and Cultural Experience All local people I interacted were exceedingly polite, often so polite that I questioned what I had done to deserve that respect. Though the language difference was sometimes a barrier, most people understood and spoke enough English for basic communication. I also am grateful to the University of Tokyo for offering a summer beginners Japanese language course to foreign students. This course helped immensely, especially when traveling outside Tokyo. Travel was very convenient via subway and rail cars. I had a JR pass, which gave me 7 days of unlimited access to a certain set of trains across Japan, which proved a worthy return on investment. I was pleasantly surprised by the simple, yet intricate beauty of the Japanese culture. These simple aesthetics are demonstrated in areas ranging from Japanese cuisine to the tatami mat floored rooms. This culinary skill was evident everywhere I ate in Japan, and I am now convinced it is the country with the best food. Another example of this simple beauty are the torii gates found in the Meiji Shrine, atop Mt. Fuji, and displayed in vermillion brilliance at the Fushimi Inari Shrine in Kyoto. The service I received was excellent and a highlight of my time in Japan. Food in restaurants came within minutes, in drastic contrast to most American restaurants. The level of hospitality I was shown when I stayed in a ryokan, a traditional Japanese inn, had me feeling embarrassed. The tatami floored rooms were pristine, the traditional kaiseki dinner was delicious, and our host even walked to us to bus stop the next morning. I am humbled by both the beauty of Japan and the hospitality of its people. Needless to say, this was a valuable cultural, professional, and personal experience.

6 Acknowledgements

This work was funded by the Princeton/University of Tokyo Educational Partnership in Plasma Physics (PUTEP). This program consists of two weeks of introductory plasma physics lectures at PPPL and six weeks of training at the University of Tokyo. I thank all those who made this program possible. Furthermore, I thank my advisor for this project Professor Masahiro Hoshino and his lab group for their guidance and advice.

6 Princeton-UTokyo Educational Partnership Report Phillip Dang Princeton University Physics Department This summer, I was fortunate enough to participate in a partnership program between Princeton University and University of Tokyo to study and do research on plasma physics. Firstly, I'd like to express my gratitude to Dr.Yamada, Professor Ono, Professor Shimizu for their mentorship and for organizing and guiding this wonderful program. I'd also like to thank Dr. Lee and all members of the Hinode group at ISAS for their warm welcome and support during my stay there. And finally, I'd like to thank all members at PPPL who helped make this program possible. Research Report I'd like to briefly report my research on plasma diagnostics using flare data observed by EUV(extreme ultraviolet) Imaging Spectrometer- or EIS. EIS is one of the instruments of the Hinode sattelite. Using the spectroscopy, we can measure the solar plasma properties, electron densities, temperature, and dynamics, etc. The methods are same for different data sets. However, for this report, I will use the flare data set observed by EIS in Januaray 2014.

Fig.1 Top: Line intensity, line velocity and line width (FWHM) Bottom: Fitted Spectra commpared with original data 1. Calibration In general, EIS data should be calibrated before we look at it. This is because EIS data are affected by warm pixels on the CCD which make it difficult to study the images. These "missing data" arise from a variety of causes, including saturated data, detector artifacts (dust, warm pixels, hot pixels), cosmic ray hits and missing data packets. Thus I firstly learned to flag these "missing data" using SolarSoft. Each pixel in the data array will have an intensity and error value. The intensities of missing pixels are interpolated from neighboring pixels. 2. Deriving intensities, velocities, and linewidth maps Next, I learned to fit data at each pixel in the image (see Fig.1 and Fig.2). Generally the EIS emission lines have a Gaussian shape and, by fitting a Gaussian function to the spectrum, we can derive line intensity, line width and velocity maps. Velocity and line width maps can be determined by looking at the doppler shift of the lines 2014 January 13 21:50:44 UT Flare Data Fe XII 186.88 Intensity Velocity Linewidth

Fig.2 Fit data by Gaussian-fitting at each pixel in the raw image. Velocity and linewidth maps are determined from the Doppler shift of the line.

One typical source of error that can arise is when there are multiple emission lines in a window, or lines blending. This error can significantly change the fitted value for intensity and thus affect other important pieces of information like density and temperature (as we'll see later) 3. Density Diagnostics In order to extract density, I will briefly discuss line radiation and a few useful quantities such as flux and contribution function. 3.1 Line Radiation In most cases, the solar atmosphere is optically thin and so that all the photons emitted along the line of sight eventually reach the observer. Under these conditions, the number of photons in a spectral line will be given simply by the sum of all contributions of the plasma along the line of sight. The power emitted by a volume element dV by the transition j --> i in the ion X+m and observed at a distance d by a detector with collecting area S is given by:

+m where vij is the frequency, Aij is the Einstein coefficient for spontaneous transition and N(Xj ) is the density of emitters. Integrate along the line of sight:

Define flux as

3.2 Contribution Function The density of emitters can be expressed as a function of the electron density using the relation:

Using this expression, we can define the contribution function G(T, Ne) as

The contribution function G(T,Ne) includes all the atomic physics involved in the process of line formation and, once all the relevant rates are available, it can be calculated theoretically as a function of electron density and temperature.

3.3 Density Map There are different ways to measure electron density. For this research, I learned to measure it using the flux ratio of two spectral lines.

Most coronal lines are optically thin and so the measured line intensity is directly proportional to the emissivity, which means that the measured intensity ratio can be converted to a density using the emissivity ratio plot. After performing Gaussian fits to the two emission lines of the density diagnostic, I used the theoretically calculated line ratio with density to derive density map (see Fig.3)

Fig.3 Left: Theoretical variation of the line ratio with density using CHIANTI database. The spectral lines ratio used is Fe XII 192.39/Fe XII 186.88. Right: Density map derived from Gaussian fits of 13-Jan-2014 21:50:44 UT Flare Data and theoretical flux ratio on the left

4. Thermal structure/Temperature diagnostics I will now derive another useful quanity needed to extract plasma temperature, namely emission measure (EM) Earlier, we expressed flux F as

This quantity can be measured in both isothermal and multi-thermal plasma

4.1 Isothermal case (EM Loci Method) When the plasma is approximately isothermal, the measured flux can be written as

where d is the distance between the observer and the source, and G(Tc) is the contri- bution function of the line, calculated at the plasma temperature Tc. Thus, the function EM(T), also called EM loci becomes

The emission measure diagnostic technique consists of displaying all the EM(T) curves calculated from the fluxes of a set of observed lines from many different ions in the same plot as a function of temperature: all the curves will meet in the same point (Tc, EM), unless their contribution functions have atomic physics inaccuracies, or the lines are blended with lines from other ions. The single crossing point determines simultaneously the plasma temperature and emission measure, and its presence implies an isothermal plasma (see Fig.4 for an example)

Fig.4 Emission measure analysis of Si lines emitted by Si VIII to Si XII. Left: Isothermal plasma from the quiet solar corona: the common crossing point is indicated by the dashed lines Right: multithermal plasma: no single crossing point can be defined. 4.2 Multithermal case (no clear crossing point) Having done the analysis for isothermal cases, I also learned to diagnose multithermal plasma. Define differential emission measure (DEM) such that

There are different methods to invert this equation for observed fluxes and known G(T) to determine plasma temperature. In this research, I learned to use the Monte Carlo technique which utilized a statistical approach based on a Bayesian statistical formalism that allows the determination of the most probable DEM curve that reproduces the observed line °uxes.

Fig.5 Left: Emission measure for 13-Jan-2014 21:50:44 UT Flare Data. Right: Best DEM curve to produce the EM and observed line fluxes using the Monte Carlo techniques 5. Summary and Acknowledgement Flares on limb show the loops and their structure quite clearly. I'm currently using other data sets from EIS (9-minute interval) to study the temporal variation of plasma properties in loops. I've become very interested in studying sudden bursts of energy in the Sun, i.e. flare and coronal mass ejection (CME), particularly the loop structures for flares on the limb. I'd really like to study and understand the underlying physics that drive these processes. One very interesting topic for me is to explore how magnetic energy stored in the corona is released to produce flare. The timescale over which flares occur and the energy they release are particularly interesting to me. I also fortunate enough to attend ISAS open campus and saw many interesting researches in solar/plasma physics. In doing EIS analysis, I've come to appreciate the difficulty and limitation of solar observations. I'd also like to study numerical simulations of the solar atmosphere, particularly the MHD numerical simulation of flare and CME. Finally, I'd like to express my gratitude for everyone who made this wonderful program possible. Over the course of this program, I met and learned from many wonderful Japanese scientists who taught me many things about physics and Japanese cultures. I've come to really appreciate Japanese work ethics, cultural values, and am very motivated to continue studying plasma physics.

Camille Rullán Princeton University

Post-Internship Report

I would like to start off my report by thanking the people that made this exchange possible: Dr. Yamada and everyone at PPPL as well as Dr. Ono and his lab. I am grateful not only for the opportunity to travel to a new country, but to learn a discipline that was so new to me and be able to do so alongside people who are passionate about what they do and about sharing that knowledge. I would also like to thank Dr. Ono and Dr. Ji for accommodating my request to do research for my Junior Paper over at the UTokyo. I would be happy to share the finished report.

Research Activity I went into this internship with no previous working knowledge of plasma physics, just curiosity and willingness to learn. The summer school at PPPL did a great job of putting us up to speed in the field. There was a lot of material to cover, and the days were long, but I ended up learning much more than I anticipated. The last section of lectures, where it was just the UT/Princeton exchange students, I naturally found both more interesting and more useful as it related directly to our coming projects. If I were to give one suggestion to the program it would be to have the students chose, or know more or less, which project they would be working on during the internship. That way they could know which information is the most important from the lectures and also be able to better prepare beforehand. I found it difficult to decide which graduate student to work with at UTokyo, since I didn’t really know what everybody was doing. That made the first week a little bit slow, as it was spent reading and talking to other lab members. Once I had a project, though, things started to go much more quickly and I got very into my work. I chose to work with Xuehan Guo on his idea to make a magnetic probe to measure the current sheet width. We spent the first two - three weeks building the probe and understanding the experimental plan. The probe we built is T-shaped with 13 poloidal field copper coils and 2 to measure the toroidal field to assure proper alignment. We installed the probe in UTST so that the coils would be along the x-point and we could measure the change of the magnetic field over time. Over more than a week, we gathered a good amount of data. Guo explained the theory needed to extract the time evolution of the current sheet width, and we were able to get some preliminary analysis done. I found the project challenging, but in a good way. I will continue to be in contact with Guo throughout the semester so that we can continue this analysis. I would have of course liked more time to collect data and solve some little problems, but this is usually the case in research, and I think I have sufficient and good data to write my JP. I was very satisfied with my project. I found it to be interesting, of course, but I particularly enjoyed the hands-on engineering challenge. It was different from any work I had done - my studies tend to stay more in the theoretical side - and it was satisfying to see the idea of the probe become something real and functional. I think one of the main differences between labs at UTokyo and Princeton (although I do not have experience working at PPPL so I cannot say for sure) is that the students at UTokyo enjoy making their equipment. They take pride in building their experiments from the ground up, and it results (for them as well as for me) in a very thorough understanding of the project. I could not have been happier with Guo as a mentor, either. He was very welcoming and friendly, as well as a great teacher. It was fun to work with him, even at late hours or at moments that it seemed the project was not going to work. Although he left for the space of a week to a summer school, he made sure that other members of the lab could help me out. It was very nice of other lab members to step in and help me while Guo was out, and I found that the lab in general had great atmosphere of collaboration. I found the lab members to be shy at first, but always welcoming. I enjoyed having lunch with them every day and going to the welcome/farewell dinners. I made good friends, and it was great to work in an environment where people were happy to be there. I usually worked from 10 until the evening, the last week sometimes going until 10-11pm, but I never really minded since I was so involved in my project and the other lab members were so nice.

My experience in Japan I won’t go into a long and detailed comparison of Japan and the US/Puerto Rico (my home), since that could take up a whole book, so I will include some short reflections. But I did truly love it and I cannot wait to go back soon. The program did a great job with housing for Samantha and I. We found all the hotels to be very comfortable. Mitsui Garden in particular was lovely. It was great to have a kitchen and be so close to a supermarket (and an onsen!), and the room was quite comfortable. The short Japanese course was also helpful, since I think it is important, when traveling to another country, to learn as much of their language as possible. Not only for basic survival, but also to be polite and appreciative of the culture as well as to have a more complete immersion. I think the Japanese language is beautiful and although it is very hard for me to learn, I may start taking it at Princeton soon. The language barrier was the only frustrating part about the stay. I wish I had spoken more Japanese so I could have made better connections with the people around me. Reading menus was almost impossible and I would get lost sometimes, but I found that the Japanese people I encountered were very welcoming, honorable and willing to help me out. One of my favorite parts of being in Japan was the food. I knew little about Japanese cuisine (besides sushi and tempura) so I had a great time discovering new dishes. I decided I would try everything that was placed in front of me and always ask for recommendations, and it was a great strategy for discovering dishes I would have not normally tried. I really appreciated when Dr. Ono and our lab mates took us to meals, since they knew what was best to eat. My favorite dish is ramen, and I am currently lamenting the lack of good ramen near me. I also loved Tokyo, and I felt like I could have stayed there for a year and never have discovered everything. I found it to be a fascinating and fun city. To appreciate as much of my time in Japan as possible, I traveled with some of the other Princeton students around to places such as Kamakura and the Chiba Peninsula. Samantha and I also took a longer trip after the end of the internship to Kyoto, Nara, Hiroshima and Osaka. I would have loved to stay longer, but this trip was a great taste of Japan and I will surely be back again. Princeton/UTokyo exchange summary Samantha Cody

In this summary I will first provide the details of my work, followed by an account of my general lab experience and my personal cultural experiences in Japan.

Project summary: Soft X-ray measurements on UTST device

Introduction

The UTST laboratory at the University of Tokyo is invested in the study of magnetic reconnection, a phenomenon that occurs in the magnetospheres of both the Sun and the Earth, and can be reproduced in an experimental setting when two plasmas are merged within a confinement chamber. As the magnetic fields of the two plasmas approach one another, the topology of the field lines is altered; anti-parallel field lines connect at a central reconnection point, named the "x point", and the connected field lines are pulled outward, causing plasma acceleration and ultimately heating.

Specifically, the UTST group seeks to understand a number of different plasma diagnostics under reconnection conditions in order to better understand the mechanisms of reconnection as well as the properties of confined plasmas. There are a variety of probes installed in the UTST device, intended to measure different properties, such as the natures of the toroidal and poloidal magnetic fields; the strength of the reconnection electric field; electron temperature, velocity, density, current density; and so forth.

One particular phenomenon of interest is that of X-ray radiation from the plasma. There are three different mechanisms of X-ray radiation; Bremsstrahlung(free-free) and recombination(free-bound) radiation, which both exhibit continuum spectrums, and line radiation(bound-bound), which has a discrete spectrum due to the bound states of the electrons.

Bremsstrahlung radiation is particularly interesting in the context of magnetic reconnection, as it occurs in the incident of electron acceleration. Thus, if a significant amount of radiation is detected during the reconnection period, it can provide us with information about electron behavior during reconnection, namely the nature of electron acceleration in the plasma.

Soft X-ray measurement method

During reconnection, any X-ray emissions produce a current that can be detected by a device known as the Surface Barrier Detector(SBD). In the SBD, also known as a semiconductor detector, ionized radiation is measured by determining the number of free charge carriers in the detector material. Radiation creates free electron-hole pairs, and as the requisite energy for creating these pairs is known, the intensity of the ionized radiation can be ascertained by the number of pairs detected.

SBDs are placed such that they have a viewing field which contains a poloidal cross-section of the reconnection region. Furthermore, a polycarbonate filter is placed in front of the detector in order to filter out low frequency signals.

A preamplifier is necessary to convert the current and amplify the signal detected by the SBD into a readable voltage signal. Certain factors must be taken into consideration upon the construction of such a circuit, most importantly the reduction of noise that could potentially obscure the signal. The circuit consists of three key components: an I/V converter to convert the signal to voltage, a non-inverting amplifier to amplify the signal, and a buffer amplifier to reduce impedence consequent of long transmission lines.

I/V converter

In an I/V converter, the positive input is attached to ground whilst the signal is inputted into the negative input. A feedback resistor is added, from the output to the input. The gain of the op amp is so high such that all the current must go through the feedback resistor, making the gain Vout=(Iin*Rf). However, ​ ​ ​ ​ ​ ​ increasing the feedback resistance, and thus the gain, often causes instability problems and oscillation. This problem is combatted by adding a feedback capacitor in parallel with the feedback resistor. The values of the feedback resistor and capacitor are limited by the cutoff frequency, which for the purposes of X-ray detection ought not sink below 300 kHz. The cutoff frequency is determined by the expression 1/(2*pi*R*C).

Non-inverting amplifier

The signal, converted to voltage by the I/V converter, is sent from the output of the first op amp to the positive input of the second. A feedback resistor is added, once again, from the input(negative) to the output. A voltage divider (a grounded resistor) is added to the feedback resistor, such that only a fraction of Vout is fed back to the input. The operational amplifier works to make the difference between V+ and ​ ​ ​ ​ V- 0; thus, Vout will be whatever makes the voltage across the inputs the same, or whatever voltage is ​ ​ ​ ​ required to drop Vin volts across the feedback resistor. Thus, if the voltage divider is R1 and the feedback ​ ​ ​ ​ resistor R2, the gain of this circuit is (1+R2/R1). Thus, if the R1 resistance value is made to be relatively ​ ​ ​ ​ ​ ​ ​ ​ low, the characteristic gain of this circuit can be made to be quite high, depending on/limited by the parameters of the op amp used. This element of the circuit is primarily responsible for the amplification ​ ​ of the voltage signal.

Unity gain/Buffer Amplifier

The final component of the three-part circuit is a buffer amplifier, which serves to reduce the characteristic high impedence of the circuit in order to account for the long transmission cables through which the signal must travel. A buffer amplifier is essentially a voltage follower; a large problem inherent to op-amp circuits is that the impedence is incredibly high, meaning that very little circuit is drawn through the circuit. What with the length of the signal transmission cables, the signal would be too weak. A buffer amplifier has a unity gain of 1--or in other words, the op amp does not provide and amplification to the signal. Thus, the buffer amplifier draws in very little current, thereby not disturbing the original circuit, and sends the output back through a feedback loop with no resistance. Thus, the circuit outputs the same signal that is inputted, and the circuit acts as an isolation buffer.

There are a number of necessary measures to take in order to reduce noise. First, a high-performance operational amplifier was chosen, with a low input bias current and high gain bandwidth--namely, the LTC6269. Various other solutions to the noise problem were found via trial and error--for instance, twisting ground and power lines together to minimize the effects of ground loops, increasing the feedback capacitance of the first circuit, and covering the wires with aluminum foil. The effects of these small “tweaks” will be evident in the results.

Results

Below are a few of the results of my measurements, with accompanying descriptions.

This was one of the first plotted runs. As one can see, the signal--a small bump at approximately 9.5E3 ms--is barely indistinguishable from the background noise. I incrementally increased the feedback capacitance of the I/V converter, which reduced some noise, and simultaneously increased the feedback resistance of the non-inverting amplifier, which let to a much more intelligible result:

Now, there is a very obvious peak between 9.45E3 and 9.6E3 ms. There is still, however, some excess noise. Some further measures were taken, by attempting to eliminate local causes of noise near the amplifier, and the signal was improved even further:

There was no signal when no merging occured.

Discussion

To some perfunctory degree, with the time that I had, I tried to think of a physical explanation for my results. Upon comparison of my plots with plots of the toroidal electric field generated during merging, it became evident that the peak of the electric field strength was somewhat before the soft x-ray bursts I observed. One explanation I came up with for this phenomenon was that at the peak electric field strength, the electrons in the plasma were provided with a great deal of kinetic energy via acceleration by the field; and when the electric field strength abruptly dropped off, the electrons were rapidly decelerated, which provided the conditions for Bremsstrahlung radiation. Thus, the phase shift between the two peaks made sense for explaining the source of the bursts.

General

I’ve worked in a lab before, but as I begin to venture more into the world of research I am coming to understand that there will always be a host of problems that one cannot fully prepare for that will spring forth throughout the research process. So much of research seems to be about being able to act quickly and resourcefully to address unpredictable setbacks. For example, the biggest setback to my project was that my mentor, Ushiki-san, and I ordered an extremely small op-amp typically used for micro-circuits. We lacked the tools typically used to solder such small components, such as a microscope and a micro-soldering iron. After much struggling with the sheer size of the op amp, we realized we didn’t know what the configuration of the pins were--where input, output, voltage supply, etc were, and so forth. I ultimately had to scrap my entire original circuit design and start from scratch. When the circuit was finally completed, I had to do extensive troubleshooting to make sure it worked properly, and once the amplifier was functioning further measures had to be taken to reduce noise in the signal. In short, problems would crop up out of the blue, and all I could do was jump to solve them as quickly as possible. Because I cared about the project, it wasn’t a chore to spend a lot of time working. If something wasn’t functioning properly, it was more gratifying to keep trying to fix the issue than to give up and try another time. I learned a great deal and had a genuinely good time through the process, stressors and all.

Of course, while I was spending a great deal of time in the lab, I was also exploring the environment around me and trying to learn something about the new world I was inhabiting. Japanese culture is fascinating and different. The US is such a young country, and such a mixing pot, that many people joke that it has no culture at all. Tradition doesn’t play a particularly large role in day to day life. In Japan, however, culture and tradition seem extremely present in everyday life. There were many small, subtle things that I had to learn about Japanese culture, including things that were impolite, or other things that were expected of me. I was able to try a variety of Japanese foods, all of which I loved, and to marvel at the enormity and modernity of Tokyo. The members of the UTST lab treated us with great hospitality, making us feel welcome and teaching us various aspects of Japanese culture. I honestly loved my time in Japan and hope that I’ll be able to go back as soon as possible, and I very much hope I can visit many people I met at the the UTST lab again. Guide-Field Reconnection in MRX

Xuehan Guo

November 29, 2016

1 Introduction

Magnetic reconnection, [1, 2] which changes the topology of magnetic field lines, provides a new equilibrium configuration through magnetic self-organization. Guide field, the component of magnetic field which is perpendicular to the reconnection plane, plays an important role in the dynamics of reconnection. Most instances of reconnection in nature [3] and the laboratory [4] contain a significant guide field (Bg) in com- parison with the reconnecting field strength (Brec), prompting the study of this type of reconnection both theoretically and numerically [5]. In magnetosphere reconnection, for example, guide fields often reach the level of the reconnecting field (B B ), while reconnection in fusion experiments (such as during toka- g ∼ rec mak or reversed-field pinch sawteeth) can have guide fields exceeding 20Brec. The large reconnection electric field along the magnetic field lines often accelerates electrons to super-thermal speed, causing a significant amount of high energy tail (runaway) in their electron energy spectrum during reconnection events of solar flares and tokamak sawtooth. The energy conversion mechanism of magnetic reconnection is a key issue to solve.

2 Experimental Setup in MRX

(a) Magnetic Probe Array Equilibrium Field Coil

(b) Magnetic Field Lines TF

37.5cm PF

Flux Core R Current Sheet

Y Z Guide Field Coil Current

Figure 1: (a) The picture shown is a cross-section of the cylindrically symmetric vacuum vessel with magnetic field lines drawn. (b) Each flux core contains a PF winding to produce the magnetic X-point geometry and a TF helically wound coil, which produces an electric field used to break down the plasma. .

Experimental studies described in this report were carried out on the MRX at the Princeton Plasma Physics Laboratory (PPPL). MRX is a mid-size laboratory device specifically designed for detailed studies of mag- netic reconnection. MRX has the unique ability to create discharges with a negligible guide field. MRX also has versatility in controlling external experimental conditions such as the system size L and the magnitude of the guide field. Figure 1(a) shows a cutaway view of the MRX vacuum chamber. The local coordinate

1 system used throughout this paper is also shown: R is radially outward, Y is the out-of-plane (symmetric) direction, and Z is the axial direction. The gray circles in Fig.1(a) indicate the cross sections of the donut- shaped ”flux cores” inside of which there are two sets of coils: poloidal field (PF) coils and toroidal field (TF) coils, as shown in Fig.1(b). Extensive sets of diagnostics are employed to study guide-field reconnection in MRX. Due to the relatively low electron temperature and short discharge duration (< 1 ms), in-situ measurements of plasma quantities are possible in MRX. The evolution of all three components of the magnetic field is measure by a 2-D magnetic probe array, which consists of 8 probes with a separation of 3 cm along Z. Each probe has 35 miniature pickup coils with a maximum radial resolution of 6 mm. The triple Langmuir probes, which do not require a sweep of the bias voltage, are used to measure both the electron temperature (Te) and density

(ne). A fluctuation probe is utilized to measure fluctuations in all three components of the magnetic field and in the out-of-plane component of the electric field.

3 Experimental Result

Figure 2(a) shows the current sheet structure in the quasi-steady state of guide-field reconnection. The current sheet is elongated along one separatrix arm due to combination of the Hall effect of the guide-field. Figure 2(b), (c) and (d) show the profiles of electron temperature, energy in high-frequency (0.8 to 18 MHz) magnetic fluctuation and the out-plane current density along along the illustrated cut in Fig.2(a). We observed that localized electron heating at the X-point and the high electron temperature area in sharp contrast with out-plane current density profile. Meanwhile, we observed localized magnetic fluctuation in Lower-Hybrid frequency range ( 10 MHz). Furthermore, this electron heating has a strong correlation on ∼ the guide-field ratio (Fig.2(e)). These electron heating results are consistent with the other strong guide-field reconnection experiment in UTST [6] and MAST [7] devices.

(a) Jy (MA/m 2 ) 0.435 0 (b) 0.415 -0.1 15

0.395 -0.2 0.375 10 Te [eV] R [m]

-0.3 0.355 -0.4

0.335 5 ] 3 0.315 -0.5 -0.05 0 0.05 0.1 (c) J/m 4

Z [m] -3 10

(e) × 2 [

25 0 µ

/2 0 20 2 dB 0 δ z [m]

15 ] 2 -0.1 (d)

Te [eV] 10 -0.2 Jy [MA/ m

5 -0.3

-0.4 0 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 01234 Bg /B rec δ R (distance from the X-point) [m]

Figure 2: (a) The magnetic flux (line contour) and out-plane current density (color contour) in the quasi- steady state of guide-field reconnection. The profiles of (b) electron temperature, (c) energy in high-frequency (0.8 to18 MHz) magnetic fluctuation and (d) out-plane current density along the illustrated cut (Z = 0). The δR is the distance from the X-point. (e) The correlation between the electron temperature near the X-point and the guide-field ratio. .

2 4 Discussion

Since the electron temperature profile is similar to the magnetic fluctuation power profile, the fluctuation in Lower-Hybrid range is probably related on the electron heating in the strong guide-field reconnection. Because of the out-plane reconnection electric field and the out-plane guide-field, the parallel electric field exists within ion sound Larmor radius, which is about 2 3 cm in this experiment. This parallel electric field ∼ would easily accelerate the electrons during the strong guide-field reconnection. When there is a fluctuation which can be coupled with electrons, the accelerated electrons would be thermalized through the wave particle interaction near the X-point. Therefore, the observed fluctuation may generate anomalous resistivity, which thermalize the accelerated electrons as well as sustain the reconnection electric field near the X-point during the guide-field reconnection.

5 Summary

During the strong guide-field magnetic reconnection in MRX device, we observed the electron heating near the X-point and the high electron temperature area in sharp contrast with the out-plane current density profile. The observed electron heating agrees with the previous strong guide-field reconnection experiment in UTST and MAST device. Meanwhile, we also observed strong magnetic fluctuation in Lower-Hybrid range that may generate anomalous resistivity, which thermalize the accelerated electrons as well as sustain the reconnection electric field near the X-point during the guide-field reconnection. We need further experimental measurements for the fluctuation (phase velocity measurement) to distinguish the fluctuation and study a role of the observed fluctuation in electron heating and balancing the reconnection electric field field at the X-point during guide-filed reconnection.

Acknowledgement

I am using this opportunity to express my gratitude to everyone who supported me throughout the Princeton- Univeristiy of Tokyo exchange program. I deeply thank to Drs. Masaaki Yamada, Hantao Ji and Jongsoo Yoo for their many helpful advices during the stay at PPPL. I would also like to thank Professor Yasushi Ono who made a lot of effort for me to materialize this stay.

References

[1] M. Yamada et al., Rev. Mod. Phys. 82, 603 (2010).

[2] E. G. Zweibel and M. Yamada, Annu. Rev. Astron. Astrophys. 47, 291 (2009).

[3] J. P. Eastwood et al., Phys. Rev. Lett. 104, 205001 (2010).

[4] J. Egedal et al., Phys. Rev. Lett. 98(1), 15003 (2007).

[5] Cassak and J. F. Drake, Phys. Plasmas 14, 054502 (2007)

[6] X. Guo et al., Phys. Plasmas 22, 101201 (2015)

[7] H. Tanabe et al., Phys. Rev. Lett. 115, 215004 (2015)

3 Work at PPPL Taishi Kaneda

During my 4-week stay in Princeton, I was assigned to the MRX (Magnetic Reconnection Experiment) team at PPPL (Princeton Plasma Physics Laboratory) and worked on circuit design of a Langmuir probe for the next-generation device, FLARE (Facility for Laboratory Reconnection Experiments), under the guidance of Dr. Jongsoo, who is a postdoc researcher of MRX. In the first week, after taking safety tests, I was taught how to diagnose plasma with a quadruple Langmuir probe, which is composed of double probe and two floating probes, and was supposed to use to measure the density and the electron temperature of plasma in the FLARE. After I understood the necessity of electrical isolation and linearity between input and output, I studied about the operating principle of optocouplers which could be used to meet the requirements. In the second week, I started circuit simulations with LTSpice and tested the electrical function of optocouplers. I also tested a fundamental circuit which was drawn on the datasheet of an optocoupler. It is shown in Figure 1. Arranging circuit elements like this, you can get output voltage (Vout) which is equal to (R2⁄)R1 Vin. I had trouble using the circuit simulation software, so I could not make as much progress in this week as I had expected (or had been expected). In the third week, I optimized the circuit adding some circuit elements to it. The optimized circuit including electrodes part is shown in Figure 2. Capacitor C1 is added to prevent the electrical signal from oscillating. R3 is a current limiting resistor which limit the current through LED to less than the rated input current of LED. The right op-amp forms a LPF by the addition of capacitor C2. Then I looked for the most suitable optocoupler and op-amps. As a result of consideration of bandwidth, slew rate, ease of use and so on, I chose HCNR201 (Avago Technologies) and ADA4891-1 (Analog Devices). Using these ICs I simulated the optimized circuit and determined the value of each element so that the circuit could work properly at up to around 5 MHz. In the end, the bandwidth (-3dB) of the whole circuit reached 5.6MHz. In the final week, I gave a presentation about this circuit to members of the FLARE team and discussed it. After that, as the last task, I handed over the results to one of them. The circuit I designed and optimized was supposed to be used as a prototype of the probe which would be inserted in the FLARE. Figure 1

Figure 2 Correlation between outer gap and plasma stored energy during Neutral Beam injected from different sources in NSTX-U

Yoshiyuki Tajiri1 , Rory Perkins2 Masayuki Ono2

1 University of Tokyo , Kashiwa-shi , Chiba 2 Princeton Plasma Physics Laboratory , Princeton , New Jergy

Backgrounds and Motivation To understand what contirbute to change the Compared with conventional torus device, midplane outer gap, it is important to look some Spherical Torus has low aspect ratio and high parameter such as plasma stored energy and im-

β, because β is in inverse proportion to aspect purity, βp and so on. rationA. Now, Aspect ratio A is defined as NSTX-U

A = R0/a (R0:major radius , a:minor radious). The National Spherical Torus Experiment Up- To decreace the aspect ratio A, non-inductive grade (NSTX-U) is constructed to study the plasma ramp up is important for economical re- physics principles of spherically shaped plasmas. actor. In NSTX-U, we plan to generate the plasma which is strongly coupled with HHFW and NBI. For this reason, new NBI device was installed in NSTX-U, and total of NBI beam line is six. (See Fig.1)

Fig.3 Overview of NSTX-U

Overview of Experiment This experiment was conducted to evaluate parameters of the plasma when Neutral beam Fig.1 Geometory of new NBI beam lines was injected indivisualy from different sources (each beam at 1MW). The shot numbers of Then, the midplane outer gap which is this experiment are # 204713 (Black line in cosidered as important parameter of plasma plots.Port 2C was used.) and # 204714 (Blue boudary shape vary by using different NBI line in plots.Port 2A was used.), # 204715 (Red sources.(See Fig.2) line in plots.Port 2B was used.), # 204716 (Or- ange line in plots.Port 1A was used.), # 204717 (Yellow line in plots.Port 1C was used.), # 204718 (Deep Orange line in plots.Port 1B was used.).Each indivisual beam was injected from 0.5s to 1.3s. Results These are plots of outergap (black line) and Fig.2 The midplane outer gap with the stored energy (blue line), poloidal coil current plasma used different NBI sources (red line).

1 Fig.4 beam line 1A Fig.8 beam line 2B

Fig.5 beam line 1B Fig.9 beam line 2C

We can see that the plots of outergap with NBI (1A and 1C, 2A) rise. Conclusion The results of this experiment suggest that there is a phenomena which cause increasing outergap. The picture below shows the geome- tory of NBI beam line and RF antenna.

Fig.6 beam line 1C

Fig.10 beam line and HHFW antenna

Fig.7 beam line 2A NSTX-U inject Neutral beam toward HHFW antenna. So I cosider that the outergap increase because of the geometory of NBI beam line and

2 HHFW antenna. Future work I will study the ray of Neutral beam and the beam line strike the antenna. Further, I want to investigate impurity data of spectroscopy when NB is injected indivisually.

3