Cover-Relevance of Advanced Nuclear Fusion Research

"Relevance of Advanced Nuclear Fusion Research: Breakthroughs and Obstructions"

Bruno Coppi

Massachusetts Institute of Technology

Norman Rostoker Memorial Symposium University of California, Irvine, 24-25 August 2015

Fusion Reactions to be Exploited

(with existing technologies in order to produce basic knowledge of high energy plasmas and to attempt realizing a net energy generation system)

D-T

D-D

D-3He

p-11B

2 Advancements in nuclear fusion research are rated in terms of criteria (but not all) to be met in order to achieve DT ignition conditions.

D + T → 4 He + n

simplified ignition condition

Te ! Ti

nD + nT = ne

3.5 MeV εα !

4 Example of Illusions (emerged at the time of the AEC to ERDA to DOE Transitions)

• To produce an energy generating system skipping the basic plasma physics research that a good scientific tradition would suggest

• To underestimate the consequences of not valuing an adequate understanding of high energy plasmas and the benefits of advanced technology developments (e.g. high magnetic fields) spurred by fusion research

3 Scalings

2 σ v F ∝Ti in the range of temperature of interest

(parameter of merit) nTτ E ≡ PM

8π ⎡n(Te + Ti )⎤ nT ! β B2c β = ⎣ ⎦ e p p 1 p 2 Bp

τ ! nα1 Bα2 I c e p 2

A combination of high poloidal fields (Bp) and total plasma current (Ip) is the indicated prescription. Note that the reactivity scales as

5 On the other hand besides avoiding these illusions, a relatively wide spectrum of approaches and, consequently of constructed and operated machines, should be developed (rather than suppressed).

For instance i) the high density, high field approach to get near ignition conditions, (e.g. Ignitor) ii) plasma confinement configurations sustained by the injection of high energy particle populations etc. (e.g. Trialpha, U.S., G.D.T., Russia) iii) steady state confinement experiments (e.g. Tokamak Energy, U.K.) 6 Additional Remarks

• Purity Requirements

• Attaining the ideal ignition conditions as an intermediate but necessary goal

• Fusion with Polarized Nuclei

Model for Pulsars (Bright Spot) (corresponding to a local dip in the transverse thermal conductivity)

B Be ! z

2 2 0 1 ⎛ ∂ D⊥ ⎞ 2 ∂D⊥ ⎞ ∂ D⊥ ⎞ D D ; 0; 0 ⊥ ! ⊥ + ⎜ 2 ⎟ (ℓ − ℓ 0 ) ⎟ = 2 ⎟ > 2 ⎝ ∂ℓ ⎠ ∂ℓ ⎠ l=l ∂ℓ ⎠ 0 l=l0

Oversimplified Thermal Energy Balance Equations

T ! T" ℓ − ℓ , x = x exp ⎡γ t + ik x − x ⎤ e e ( 0 0 ) ⎣ ⊥ ( 0 )⎦

Model for Pulsars (corresponding to a local dip in the longitudinal thermal conductivity)

B Be ! z

2 0 1 ∂ D! 2 D! " D! + 2 (x − x0 ) 2 ∂x

Oversimplified Thermal Energy Balance Equations

ˆ dS ˆ dS S = Ti where > 0 dTi dTi

Figure 1. Vertical cross section of the Ignitor machine as presently designed External Electromagnetic Poloidal Coil radial press (n° 9-14) (n° 15, 16)

Bracing ring

Plasma Chamber

Toroidal Field Coil

Central Solenoid (n°1-8)

Figure 2. Sketch of the vertical cross section of the Ignitor machine where the main components are indicated. 12

External Electromagnetic Poloidal Coil radial press (n° 9-14) (n° 15, 16)

Bracing ring

Plasma Chamber

Toroidal Field Coil

Central Solenoid (n°1-8)

FIG. 1. Vertical cross section of the Ignitor FIG. 2. Sketch of the vertical cross section of the Ignitor machine as presently designed. machine where the main components are indicated.

FIG. 3. “Bucking and Wedging”solution. The objective is to minimize the unbalance between the principal stress components.

FIG. 5. Plasma chamber with access ports. FIG. 4. View from above the core of the Ignitor machine. The subdivision of it into 12 modules is evident. TABLE I: EXAMPLE OF PLASMA PARAMETERS [1] FOR AN 11MA OPERATIONAL SCENARIO (JETTO CODE).

11th European Conference on Applied Superconductivity (EUCAS2013) IOP Publishing

Journal of Physics: Conference Series 507 (2014) 032030 doi:10.1088/1742-6596/507/3/032030

The forces in the outer joint are supported by bolts. A steel tension ring supports the upper leg on the top joint. The forces in the central column are supported by wedging of the TF coils against each other, and by buckling against the central solenoid. The central solenoid is filled with a fiberglass/epoxy plug to reduce the maximum stresses in this region.

Figure 1. Schematic design of the TF coil system. (Left) assembled; (right) disassembled. The structure is made of stainless steel 316LN, the cables are YBCO conductors. The central solenoid is filled with a fibreglass/epoxy plug to take the compressive loads on the inside.

A finite element method (FEM) simulation of the Lorentz loads in the TF coils was made to estimate the stresses in the structure. The model is half a single TF coil. The load in the coils is due to the Lorentz force in the conductors due to the toroidal magnetic field generated by all 18 coils. Roller boundaries simulate the rotational symmetry, and the contact between the two legs. The simulation results are shown in figure 2. The maximum stress in the structure is approximately 700 MPa and the yield strength of stainless steel 316LN is larger than 1000 MPa [2], which gives a safety factor of approximately 1.4.

1 GPa

0.5 GPa

0 GPa

Figure 2. Results of FEM simulation of the stresses in the TF coils. (Left) bottom leg; (right) top leg. The colors represent the von Mises stress. The safety factor is approximately 1.4 in the worst areas.

To provide the 9.2 T on axis, a current of 8.4 MA turn is required in each TF coil. The current is carried by 70 kA YBCO cables; each cable composed by 250 YBCO tapes (25 mm width) assembled using the Twisted Stacked Tape Conductor method [3]. The superconductors are cooled with liquid

11th European Conference on Applied Superconductivity (EUCAS2013) IOP Publishing

Journal of Physics: Conference Series 507 (2014) 032030 doi:10.1088/1742-6596/507/3/032030

Demountable Toroidal Field Magnets for Use in a Compact Modular Fusion Reactor

F. J. Mangiarotti*, J. Goh, M. Takayasu, L. Bromberg, J. V. Minervini and D. Whyte Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

*E-mail: [email protected]

Abstract. A concept of demountable toroidal field magnets for a compact fusion reactor is discussed. The magnets generate a magnetic field of 9.2 T on axis, in a 3.3 m major radius tokamak. Subcooled YBCO conductors have a critical current density adequate to provide this large magnetic field, while operating at 20 K reduces thermodynamic cooling cost of the resistive electrical joints. Demountable magnets allow for vertical replacement and maintenance of internal components, potentially reducing cost and time of maintenance when compared to traditional sector maintenance. Preliminary measurements of contact resistance of a demountable YBCO electrical joint between are presented.

1. Introduction The recent development of YBCO superconducting tapes and cabling methods could be a revolutionary development for magnetic fusion. Subcooled YBCO has larger critical current density at high magnetic fields (more than 20 T) than low temperature superconductors (LTS) such as Nb3Sn and NbTi. Also, YBCO can be operated at higher temperatures than LTS, reducing the thermodynamic cooling cost and allowing resistive loss in the coil joints. An innovative concept of fusion reactor has been developed in 2012 by the MIT Fusion Reactor Design course, partially inspired by the Vulcan concept design [1]. A comprehensive report of the characteristics of the reactor is expected to be published later this year. The reactor is 3.3 m in major radius and operates in steady state. The magnetic field on axis is 9.2 T. The tritium breeding blanket is entirely made of liquid FLiBe, and the toroidal field (TF) coils are demountable, allowing for vertical replacement of the internal components of the reactor. This maintenance scheme is much faster, easier and cheaper than sector maintenance, and the replaceable parts such as the vacuum vessel can be fabricated off-site with lower tolerances. We developed a concept of demountable toroidal field coils for a fusion reactor, with preliminary stress and heating simulations. We have designed demountable electrical joints for YBCO stacked tape conductors for the TF coil system, and tested a small scale prototype of the electrical joint.

2. Toroidal field magnets concept and stress analysis The TF coil system is composed by 18 demountable coils. The shape of the coils is based on the constant tension D-shape. The coil is divided in two parts, as shown in figure 1: a removable upper leg and a stationary lower leg. The legs are joined in the outer midplane, and in the top of the coils. The structure of the coils is made of stainless steel 316LN.

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd 1 From: "Bruno Coppi" Subject: [Fwd: fusion in the local paper in France] Date: Wed, August 19, 2015 3:06 pm To:

------Original Message ------Subject: fusion in the local paper in France From: "Lawrence R. Sulak" Date: Sun, August 16, 2015 6:26 am To: "Bruno Coppi" ------

Dear Bruno,

Have not talked with you for way way too long!

I'm again at CERN for the summer...

We need time together for me to get caught up. Just read a blurb in La Provence Friday re: an MIT proposal by Dennis Whyte to use HiTc magnets. Anything to it? The article also says that Lockheed-Martin is pursuing fusion. Really?

All the very best,

Larry

Lawrence R. Sulak, Myers Distinguished Professor, BU Physics; Chairman Emeritus Founding Director, BU/CERN Physics Internship Program http://physics.bu.edu/~sulak, [email protected], Skype:lsulak From: "Lawrence R. Sulak" Subject: comments from an ITER consultant: Arc at MIT Date: Sun, August 16, 2015 8:46 am To: "Bruno Coppi"

Dear Bruno,

I've asked an ITER consultant I know, about Arc at MIT. FYI, here are his comments:

> Yes, I did see this paper. I have asked for the complete paper to be > able to read the details as I do not have access to the journal. > However, from the parts that I read they are taking the 'very high > magnetic field' approach. This a well travelled path but tends to lead > to such high forces that the materials are plastic and all deformed > under the pressure and then the machine becomes inaccessible i.e. cannot > be maintained. > > They talk about being able to take the superconducting coils apart . > That issue is as yet unresolved - maybe they have a solution. > > They talk about 'current drive' being able to circumvent the problem > with cycling the magnetic field (and the forces). This has as yet not > been achieved and has remained elusive. > > They say the first wall does not consist of individual components but is > one piece. An incredible assumption. > > I see many technical issues with the proposition which only a proper > technical review will be able to assess. I must say I am very sceptical > because the problems are well known and the possible solutions have been > discussed for years.

>> ------>> Lawrence R. Sulak, CERN/FR Cell

Schematic diagram of the components of the ITER tokamak C-ITER Organization

| International Atomic Energy Agency Nuclear Fusion Nucl. Fusion 55 (2015) 053009 (12pp) doi:10.1088/0029-5515/55/5/053009 Overview of ECR plasma heating experiment in the GDT magnetic mirror

P.A. Bagryansky1,2, A.V. Anikeev1,2, G.G. Denisov3, E.D. Gospodchikov3,4, A.A. Ivanov1,2, A.A. Lizunov1, Yu.V. Kovalenko1,2, V.I. Malygin3, V.V. Maximov1,2, O.A. Korobeinikova2, S.V. Murakhtin1,2, E.I. Pinzhenin1, V.V. Prikhodko1,2, V.Ya. Savkin1,2, A.G. Shalashov3,4, O.B. Smolyakova3, E.I. Soldatkina1,2, A.L. Solomakhin1,2, D.V. Yakovlev2 and K.V. Zaytsev1

1 Budker Institute of Nuclear Physics (BINP), Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia 2 Novosibirsk State University, Novosibirsk, Russia 3 Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia 4 Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia E-mail: [email protected]

Received 29 December 2014, revised 2 February 2015 Accepted for publication 3 March 2015 Published 15 April 2015

Abstract This paper summarizes the results of experiments on electron cyclotron resonance heating (ECRH) of plasma obtained at the axially symmetric magnetic mirror device gas dynamic trap (GDT) (Budker Institute, Novosibirsk). The main achievement is the demonstration of plasma discharges with extremely high temperatures of bulk electrons. According to the Thomson scattering measurements, the on-axis electron temperature averaged over several sequential shots is 660±50 eV with peak values exceeding 900 eV in a few shots. This corresponds to an at least threefold increase as compared to previous experiments both at the GDT and at other comparable machines, thus demonstrating the maximum quasi-stationary (∼0.6 ms) electron temperature achieved in open traps. The breakthrough is made possible with the successful implementation of a sophisticated ECRH scheme in addition to standard heating by neutral beams (NBs). Another important result is the demonstration of the signiﬁcantly increased lifetime of NB-driven fast particles with the application of ECRH, leading to a 30% higher plasma energy content at the end of the discharge. All available data including the previously demonstrated possibility of plasma conﬁnement with β as high as 60%, allows us to consider fusion applications of axially symmetric magnetic mirror machines on a realistic basis.

Keywords: mirror trap, gas dynamic trap, electron-cyclotron resonance heating, longitudinal conﬁnement (Some ﬁgures may appear in colour only in the online journal)

1. Introduction are still likely to perform sufficiently well as high-power neutron sources. One of them is the open-ended plasma Currently there is growing research activity in the field of confinement system with magnetic mirrors. Pioneering studies fusion–fission hybrid reactors, which can be used in the future predicted that there are no fundamental restrictions for even the for burning of radioactive wastes, production of nuclear fuels, simplest magnetic mirror machine to operate with Q ≈ 1[4]. electrical power generation and other applications (see [1, 2] However, these values are only achievable if one can exclude for examples). The core of such a system is a high-power the influence of cold end-walls, to which plasma can flow freely neutron source, which is a D–T fusion reactor with a power along the magnetic field lines. gain factor Q ≈ 1. Among the magnetic confinement systems That being said, the considered class of magnetic mirror the tokamak concept is considered as the most promising candidate for this purpose because it is able to experimentally traps with axisymmetric magnetic fields has several advantages demonstrate the most effective plasma confinement, and to offer: the value of Q already exceeds the demands of a hybrid reactor [3]. • simplicity of design, ease of upgrade and maintenance; However, from the engineering standpoint there are, in • intrinsic mechanism of removing impurities and products our opinion, more attractive magnetic configurations which of fusion reactions;

Figure 1. Schematic of the GDT. which is the main parameter limiting the flux of the bulk plasma (MHD) stability. At first glance, implementation of such a through the magnetic mirrors. The second plasma component scheme seems to be incompatible with the declared advan- consists of fast ions produced as a result of the oblique injection tages of high-β and low transverse transport, which would of hydrogen or deuterium atomic beams into the bulk plasma. render the axisymmetric system inferior to most other open- The fast ions are confined in the adiabatic regime which means ended configurations, let alone tokamak- or stellarator-based that their movement is governed by conservation of energy concepts. and adiabatic invariants. As a result they are bouncing in a The situation changes, however, with the introduction of region between two turning points defined by effective mirror techniques which allow the effective stabilization of plasma. ratio R = 2. The energy confinement time of fast ions is To suppress transverse transport caused by MHD instabilities determined by electron–ion collisions, namely, by the electron in the GDT, a method of vortex confinement has been proposed ‘drag’ force. This time turns out to be much less than the and implemented [14]. Strictly speaking, the method is not angular scattering time. Due to this fact the fast ions have meant to suppress the MHD modes, but rather to saturate anisotropic non-Maxwell velocity distribution, relatively small them on a relatively low level by differential rotation of the angular spread and their density and pressure are peaked near outer plasma layers induced by the radial electric field. This the turning points. produces a vortex-like structure with essentially closed flux The discharge is initiated by an arc plasma gun, which lines. Implementation of vortex confinement in the GDT = at t 0.5 ms injects cold dense plasma with a temperature achieved a record for axisymmetric mirror traps value of of several eV through one of the magnetic mirrors into the β = 0.6[15, 16]. = central solenoid. At t 4.5 ms the plasma gun is shut off. In the GDT, the vortex confinement technique is realized = = NBI heating begins at t 3.7 ms and lasts until t 8.2 ms. by biasing the ring-shaped radial plasma limiters and the Particle balance during the discharge is supported by pulsed central sections of the PA units (figure 1). According to the gas valves located close to the magnetic mirror throats. The conventional scheme the limiters are supplied with a positive =− pulsed valves are opened at t 7 ms and supply deuterium (relative to the ground) potential and the central PA sections gas during the whole discharge. are connected to the ground. However, there is an alternative The electron temperature and density are measured at scheme in which the limiters are grounded and the central PA the central cross-section of the trap (midplane) by single- sections are supplied with a negative potential. The difference point Thomson scattering for r<15 cm and by a set of between these schemes in relation to ECRH experiments will probes for r>15 cm. The diamagnetic pressure (which is be discussed further. mostly contributed by the fast ions) is measured at the effective Vortex confinement results in a stable confinement of hot mirror ratio R = 2, which is a point of accumulation of fast plasma in the central core region appear to be unaffected by particles. The energy stored in fast particles is subsequently peripheral convection. A low level of instability saturation calculated from this diamagnetic signal. A set of microwave means that although plasma remains unstable in the linear diode detectors is placed inside the vacuum vessel on the wall = opposite to the microwave input window. The diagnostic approximation, even the most prominent m 1 mode is an indicator of stray microwave radiation present in the (displacement of the plasma column as a whole) is not strong vacuum chamber, which provides qualitative information on enough to affect the confinement of the central plasma. The the absorption of microwave beams in plasma during ECRH. downside of this method, however, is a significant dissipation The D–D neutron flux is measured by the scintillator-based of energy on the radial electrodes. neutron detectors placed outside the vacuum vessel. The main conclusion based on theoretical analysis [14] and experimental results [15] is that transverse losses can be limited at the level of 10–15% of the axial power loss for the 2.1. Vortex confinement and transverse transport GDT plasmas by applying the vortex confinement method. It is well known that axisymmetric magnetic mirror configu- Overhead expenses for the power supply used by this method rations are generally unfavourable for magnetohydrodynamic are in order of a few per cent compared with total plasma

PHYSICS OF PLASMAS 21, 110501 (2014)

20 years of research on the Alcator C-Mod tokamaka) M. Greenwald,1,b) A. Bader,2 S. Baek,1 M. Bakhtiari,2 H. Barnard,1 W. Beck,1 W. Bergerson,3 I. Bespamyatnov,4 P. Bonoli,1 D. Brower,3 D. Brunner,1 W. Burke,1 J. Candy,5 M. Churchill,6 I. Cziegler,7 A. Diallo,6 A. Dominguez,6 B. Duval,8 E. Edlund,6 P. Ennever,1 D. Ernst,1 I. Faust,1 C. Fiore,1 T. Fredian,1 O. Garcia,9 C. Gao,1 J. Goetz,2 T. Golfinopoulos,1 R. Granetz,1 O. Grulke,10 Z. Hartwig,1 S. Horne,11 N. Howard,12 A. Hubbard,1 J. Hughes,1 I. Hutchinson,1 J. Irby,1 V. Izzo,7 C. Kessel,6 B. LaBombard,1 C. Lau,13 C. Li,1 Y. Lin,1 B. Lipschultz,14 A. Loarte,15 E. Marmar,1 A. Mazurenko,16 G. McCracken,17 R. McDermott,18 O. Meneghini,5 D. Mikkelsen,6 D. Mossessian,19 R. Mumgaard,1 J. Myra,20 E. Nelson-Melby,21 R. Ochoukov,18 G. Olynyk,22 R. Parker,1 S. Pitcher,15 Y. Podpaly,23 M. Porkolab,1 M. Reinke,14 J. Rice,1 W. Rowan,4 A. Schmidt,24 S. Scott,6 S. Shiraiwa,1 J. Sierchio,1 N. Smick,25 J. A. Snipes,15 P. Snyder,5 B. Sorbom,1 J. Stillerman,1 C. Sung,1 Y. Takase,26 V. Tang,24 J. Terry,1 D. Terry,1 C. Theiler,8 A. Tronchin-James,27 N. Tsujii,26 R. Vieira,1 J. Walk,1 G. Wallace,1 A. White,1 D. Whyte,1 J. Wilson,6 S. Wolfe,1 G. Wright,1 J. Wright,1 S. Wukitch,1 and S. Zweben6 1MIT Plasma Science and Fusion Center, Cambridge, Massachusetts 02139, USA 2Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA 3UCLA, Institute of Plasma and Fusion Research, Los Angeles, California 90095, USA 4Fusion Research Center, University of Texas, Austin, Texas 78712, USA 5General Atomics, P.O. Box 85608, San Diego, California 92186, USA 6Princeton Plasma Physics Laboratory, Princeton, New Jersey 08540, USA 7Center for Momentum Transport and Flow Organization, UCSD, San Diego, California 92093, USA 8Ecole Polytechnique Federale de Lausanne, Centre de Recherches en Physique des Plasmas, Lausanne 1015, Switzerland 9Department of Physics and Technology, University of Tromsø, N-9037 Tromsø, Norway 10MPI for Plasma Physics, EURATOM Association, D-17491 Greifswald, Germany and Ernst-Moritz-Arndt University, D-17489 Greifswald, Germany 11Energetiq Technology, 7 Constitution Way, Woburn, Massachusetts 01801, USA 12Oak Ridge Institute for Science and Education (ORISE), Oak Ridge, Tennessee 37830, USA 13ORNL, P.O. Box 2008, Oak Ridge, Tennessee 37831, USA 14York University, Heslington, York YO10 5DD, United Kingdom 15ITER Organization, 13067 St. Paul-lez-Durance, France 16Block Engineering, 377 Simarano Dr., Marlborough, Massachusetts 01752, USA 17UKAEA Culham Centre for Fusion Energy, Abingdon, OX14 3DB Oxfordshire, United Kingdom 18MPI fur€ Plasmaphysik, EURATOM-Association, D-85748 Garching, Germany 19AllianceBernstein, 1345 Avenue of the Americas, New York, New York 10105, USA 20Lodestar Research Corporation, 2400 Central Avenue P-5, Boulder, Colorado 80301, USA 21Raytheon Co., 1151 E Hermans Rd., Tucson, Arizona 85756, USA 22McKinsey & Co., 110 Charles Street West, Toronto, Ontario M5S 1K9, Canada 23National Institute of Science and Technology, 100 Bureau Drive, Stop 1070, Gaithersburg, Maryland 20899, USA 24LLNL, 7000 East Ave., Livermore, California 94550, USA 25GT Advanced Technologies, 243 Daniel Webster Highway, Merrimack, New Hampshire 03054, USA 26University of Tokyo, Tokyo 113-033, Japan 27Facebook LLC, 1601 Willow Road, Menlo Park, California 94205, USA (Received 7 August 2014; accepted 3 October 2014; published online 25 November 2014) The object of this review is to summarize the achievements of research on the Alcator C-Mod tokamak [Hutchinson et al., Phys. Plasmas 1, 1511 (1994) and Marmar, Fusion Sci. Technol. 51, 261 (2007)] and to place that research in the context of the quest for practical fusion energy. C-Mod is a compact, high-field tokamak, whose unique design and operating parameters have produced a wealth of new and important results since it began operation in 1993, contributing data that extends tests of critical physical models into new parameter ranges and into new regimes. Using only high- power radio frequency (RF) waves for heating and current drive with innovative launching struc- tures, C-Mod operates routinely at reactor level power densities and achieves plasma pressures higher than any other toroidal confinement device. C-Mod spearheaded the development of the vertical-target divertor and has always operated with high-Z metal plasma facing components— approaches subsequently adopted for ITER. C-Mod has made ground-breaking discoveries in divertor physics and plasma-material interactions at reactor-like power and particle fluxes and elucidated

a)Paper AR1 1, Bull. Am. Phys. Soc. 58, 21 (2013). b)Invited speaker.

1070-664X/2014/21(11)/110501/50/$30.00 21, 110501-1 VC 2014 AIP Publishing LLC

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the critical role of cross-field transport in divertor operation, edge flows and the tokamak density limit. C-Mod developed the I-mode and the Enhanced Da H-mode regimes, which have high performance without large edge localized modes and with pedestal transport self-regulated by short- wavelength electromagnetic waves. C-Mod has carried out pioneering studies of intrinsic rotation and demonstrated that self-generated flow shear can be strong enough in some cases to significantly modify transport. C-Mod made the first quantitative link between the pedestal temperature and the H-mode’s performance, showing that the observed self-similar temperature profiles were consistent with critical-gradient-length theories and followed up with quantitative tests of nonlinear gyrokinetic models. RF research highlights include direct experimental observation of ion cyclotron range of frequency (ICRF) mode-conversion, ICRF flow drive, demonstration of lower-hybrid current drive at ITER-like densities and fields and, using a set of novel diagnostics, extensive validation of advanced RF codes. Disruption studies on C-Mod provided the first observation of non- axisymmetric halo currents and non-axisymmetric radiation in mitigated disruptions. A summary of important achievements and discoveries are included. VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4901920]

I. INTRODUCTION—ADVANTAGES OF HIGH transform. Plasma physics sets the upper limit for bN and the MAGNETIC-FIELD FOR FUSION lower limit for q. The overall cost for a fusion facility is proportional to the mass of the fusion “core” and thus to the While it is common and correct to frame pure plasma magnetic stored energy / R3B2. From these arguments, it is physics phenomena in terms of dimensionless plasma param- 1,2 clear that the most cost effective fusion devices would oper- eters, practical fusion energy requires prescribed levels of ate with the highest fields that can be safely engineered. On absolute performance. This can be easily understood as a several previous occasions when the U.S. was planning to consequence of non-plasma dimensionless parameters, par- build its own burning plasma devices, CIT, BPX, and ticularly the ratio of plasma temperature to the characteristic FIRE,9,10 the price to performance argument led to compact energies required for the fusion nuclear reaction (kT/Enuclear) high-field designs. Looking forward and considering the sub- and to the characteristic energies for atomic ionization, stantial costs and extended construction schedule for ITER, recombination, and molecular bonding (kT/Eatomic). The first which was designed with “well-known” moderate-field of these leads directly to the Lawson criterion for the mini- superconducting magnet technology, a development path mum ion temperature in an energy producing fusion plasma. that features higher field seems attractive. The second is important for edge plasma and plasma-wall A discussion of the practical limits for the strength of interactions and will be discussed in Secs. IAand III. magnetic field in a fusion device is beyond the scope of this Economic and engineering considerations dictate the opti- paper, but it is worth noting the opportunities presented by mum level of neutron wall loading in a fusion reactor3 (about 2 recent developments in high temperature superconductors. 3–4 MW/m ) and consequently to an optimum absolute These materials, YBCO (Yttrium Barium Copper Oxide), for plasma pressure and density. At the same time, all of the example, have demonstrated significantly higher critical cur- operating limits for a tokamak increase with the magnetic rents at fields above 20 T.11 By operating at elevated temper- field; the maximum plasma current, which largely deter- atures where heat capacities are higher, it should be possible mines confinement, and the maximum plasma density are to build magnets with field-demountable joints, allowing proportional to B,4,5 and the maximum pressure is propor- 2 6 much more favorable modes for construction and mainte- tional to B . Thus, absolute performance increases with nance. A design concept for a high-field pilot plant has been field, as does robustness against disruptions due to the prox- developed, demonstrating the advantages of this approach.12 imity of operational limits. It is worth noting that the require- A limiting factor, of course, would be the ability to provide ment for operation near an optimum density can be the mechanical support for the magnetic stresses produced problematic for very large low-field fusion reactor designs, by high-field magnets, though the design efforts described since this density range may be above the tokamak density above suggest that this should be achievable. limit.7 Prospective tokamak reactor designs like ARIES-AT assume operation near or above all of these limits8 raising A. Consequences of high-field operation in C-Mod concern about achieving this level of performance and robustness with respect to disruptions. Research at fusion- Alcator C-Mod is the third in a series of compact high- relevant absolute parameters is required since the plasma field tokamaks built and operated on the MIT campus.13,14 and non-plasma physics couple in complicated ways that are Supporting the arguments provided above, these machines well beyond our current abilities to model. have demonstrated high performance at a moderate size and The economic advantage of high fields can be under- cost—the previous device, Alcator C, being the first con- stood by considering the total fusion power from a tokamak trolled fusion experiment to exceed the Lawson product for 2 3 4 15 device, which is proportional to ðbN=qÞ R B , where bN is density times confinement. An important early goal of the the plasma pressure normalized to the Troyon limit6 and q is C-Mod program was to provide a database that is relevant to the tokamak “safety” factor, the inverse of the rotational high-field regimes. This goal encompassed support for the

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 18.4.2.1 On: Thu, 06 Aug 2015 14:49:46 110501-24 Greenwald et al. Phys. Plasmas 21, 110501 (2014)

for heating provides a particularly good platform for studies of intrinsic rotation and particle transport. Several of the dimensioned quantities, BT,ne stand well apart from other experiments, but discharges with substantial overlap in dimensionless plasma parameters are also obtainable.185,198 C-Mod provided important contributions to the H-mode confinement database. Operating at higher current and input power than other small devices, these data broke important covariances between size, current and power, the most important scaling parameters, and led to the ITER98y scaling laws.165,166 It is worth noting that the C-Mod data, used in this database, were obtained in the ELM-suppressed regimes, with dominant electron heating, low torque, Te Ti, and in a device with metal walls. All of these are ITER-typical and different from conditions behind most of the data in the confinement database. Recent results from AUG and JET find a drop in energy confinement under similar conditions,44 sug- FIG. 38. Profile self-similarity is demonstrated. Te profiles are plotted, on a gesting that ITER98 may overestimate the results that will semi-log scale for a random selections of shots and time including the OH, be obtained on ITER. L-mode, and H-modes at a wide range in density and input power. Greenwald et al., Fusion Sci. Tech. 51, 266 (2007). Copyright 2007 American Nuclear Society.185 A. Profile stiffness and temperature profile self-similarity stability threshold dependent on R/LT and a strong turbu- Early H-mode studies noted the simultaneous increase lence and transport for normalized gradients that exceed the 199 in core energy confinement and the formation of an edge threshold. These theories also predict a dependence of the transport barrier;131 however, the first quantitative studies of critical gradient length on magnetic shear; thus, the shots in the correlation between the pedestal and core transport were Fig. 38 were selected at the same magnetic field and plasma carried out in C-Mod.17 These studies found a linear relation- current. Nonlinear gyrokinetic simulations found, in fact, ship between the height of the temperature pedestal and the quantitative agreement between the experimental tempera- normalized confinement time as shown in Fig. 37, unifying ture gradient and the gradient computed to match the experi- 200 the C-Mod database across confinement regimes. It was mental heat flux. These results also help to explain the found that the correlation was due to the self-similarity of insensitivity of the L-mode confinement to impurity radia- temperature profiles. Figure 38 shows temperature profiles tion. It was observed that the L-mode confinement followed for a collection of 100 randomly chosen shots and times, at a the empirical scaling even when virtually all power was lost wide variety of plasma density, heating power, impurity con- through radiation before reaching the plasma edge, as seen in 17 tent, and regime (OH, L, and H).185 The temperature is plot- Fig. 39. Apparently even the greatly reduced levels of heat ted on a log scale, demonstrating constancy of the conduction seen for the high radiated power were sufficient to sustain the plasma near the marginal stability point. In logarithmic gradient 1/LT ¼rT/T over almost an order of magnitude variation in temperature magnitude. This result is contrast, the H-modes are sensitive to the radiated power consistent with transport theory that predicts a drift-wave

FIG. 37. The energy confinement time, normalized to the ITER89 L-mode FIG. 39. Normalized energy confinement for the L-mode can be maintained, scaling law, is plotted vs the pedestal temperature, unifying data over a wide even at very low levels of conducted power. In contrast, the H-mode con- range of parameters and confinement regimes. Reprinted with permission finement deteriorates at a high radiated power because of the decrease in from Greenwald et al., Nuclear Fusion 37, 793 (1997). Copyright 1997 pedestal temperature. Reprinted with permission from Greenwald et al., IOP.17 Nuclear Fusion 37, 793 (1997). Copyright 1997 IOP.17

Seminario UT FUSIONE

Lunedì, 30 marzo, 2015, ore 14

Aula Bruno Brunelli, Centro Ricerche Frascati

A. E. Costley, A Sykes

Tokamak Energy Ltd, Culham Science Centre, Abingdon, OX14 3DB, UK

Compact Fusion: Significant Developments That May Open a Route to Faster, Cheaper Pilot Plants and Reactors

Two recent developments may open a faster route to fusion power based on relatively small devices. A re-examination of the ITER confinement data-bases has shown that for steady state tokamaks the fusion gain, Qfus, depends only weakly on device size implying that, at least from a physics perspective, a high fusion performance can be obtained in relatively small devices [1]. This study has also shown that if the scaling of the energy confinement time is independent of beta, as demonstrated in individual device experiments, then the fusion power needed for high Qfus is considerably reduced, typically by factors of three to four. Smaller devices have less space for shielding, especially on the high field side, but if the magnets can be made using high-temperature superconductors (HTS) then less space is needed. HTS magnets can in principle be more compact as the HTS can carry higher currents under stronger magnetic fields than low temperature superconductors; and, as cooling is more efficient at higher temperatures, less shielding is required to limit neutron heating of the magnet [2]. A second development addresses this aspect. A spherical tokamak utilizing magnets made with high temperature superconductors has been constructed and is in operation – pulses of 24 hrs duration have been demonstrated – thereby demonstrating that such conductors can be used for tokamak construction [3]. Taken together these developments potentially open a faster route to conditions when burning plasma physics effects (Qfus > 5) can be explored experimentally, and/or relevant technologies can be developed and demonstrated in relatively small devices, thereby reducing the time for the full realisation of fusion power. The details of both developments are presented in this talk and how they may work in combination is described. 1. A E Costley, J Hugill and P F Buxton, “On the power and size of tokamak fusion pilot plants and reactors” Nucl. Fusion 55 (2015) 033001. 2. C G Windsor, J G Morgan and P F Buxton, “Heat deposition into the superconducting centre column of a spherical tokamak fusion plant” Nucl. Fusion 55 (2015) 023014. 3. A Sykes et al “Progress towards compact fusion energy”, Fusion Sci. Technol. (2014) (submitted).

Frascati, 23/03/15

Agenzia Nazionale per le Nuove Tecnologie, l’Energia e lo Sviluppo Economico Sostenibile Centro Ricerche Frascati, Via E. Fermi, 45, 00044 Frascati Per informazioni contattare: Maria Polidoro, Tel. 06 9400 5309; e-mail: [email protected]