The Study of the RMF Effect on the Performance of Field Reversed Configuration Thruster

The Study of the RMF effect on the Performance of Field Reversed Configuration Thruster

IEPC-2017-101

Presented at the 35th International Electric Propulsion Conference Georgia Institute of Technology • Atlanta, Georgia • USA October 8 – 12, 2017

X. F. Sun1, Y. H. Jia, T. P. Zhang, J. J. Chen Science and Technology on Vacuum Technology and Physics Laboratory,

Lanzhou Institute of Physics, Lanzhou 730000，China

Abstract: A Field Reversed Configuration (FRC) plasmoid will be formatted by applying a Rotation Magnetic Field (RMF). The azimuthal currents that driven with RMF will couple with the radial magnetic field produced from axial magnetic field gradient and then a Lorentz force(J훉×Br) created and accelerates the plasmoid to a high velocity. This potential advantage services to space thruster can produce highly variable thrust and specific impulse at high efficiency. While the critical acceleration mechanism of this method is that the plasmoid electron current can be effectively driven. This study concerns to the effect of antisymmetric and symmetric RMF antenna on the ionization of the propellant. The RMF magnetic topology and the driven electron current from two different RMF antennas are compared, and which will be useful for the optimized designing of FRC thruster.

Nomenclature

Bω = Rotation Magnetic Field

IRMF =The driven current of RMF

Jθ =The driven current density of RMF Φ =The magnetic flux F =Lorenz Force 휔 =Frequency of RMF

Br =Radial direction magnetic field r =Plasma radius ne =Plasma electron density

I. Introduction HE first time for the Rotation Magnetic Field is used to the formation of the FRC plasma was in T1960s, and the early investigated devices in Australia were called “rotamak” which chiefly serves for the nuclear fusion.1 But until late 1990s, many experimental facilities began to adapt RMF for the ______

The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8 – 12, 2017

1Engineer, Lanzhou Institute of Physics, [email protected] formatting of FRC, such as the Star Thrust eXperiment (STX),2 Translation Confinement Sustainment (TCS),3 and TCSU.4,5 The RMF acts as two roles in fusion rotamak, one is the production of FRC plasma and the other is the sustainment i.e. fusion confinement.4 The two sets of antennas with two phases will generate a transverse magnetic field (Bω). The oscillation of the antenna current will make the Bω rotates at the poloidal direction. Due to their light weight, the electrons will tie to the field lines of Bω and an azimuthal current (Jθ) is driven, while the ions are fixed.

The matched condition for the current drive of RMF is that the frequency of Bω should between the ion cyclotron frequency and electron cyclotron frequency. Besides, the electrons collisions frequency must be lower than the electron cyclotron frequency as the same time. Then, the RMF can penetrate into 6 the plasma and drive a non-inductive current (IRMF∝ω rather than Δϕ) powerfully. At present, most of the experiments of rotamaks have shown its significant advantages of RMF. It avoids the transient high voltage and large current for the ionization of the plasma. Even though the penetrated distance of RMF field is little, it can also achieve the steady state of FRC plasma.7 Moreover, the RMF peak density is much more than other FRCs.4 In general, the driven azimuthal current of RMF can reach to tens of thousands Ampere. If a radial direction magnetic field of Br is preexistence, the coupling of the current and magnetic field will produce a Lorenz Force (F=Jθ×Br) that lead to the acceleration of the FRC plasma. For that reason, the FRC concept has been employed to the space propulsion. The Electrodeless Lorentz Force (ELF) thruster based on the current driven of RMF has been experimented to accelerate the plasmoid to a high velocity.8 Several kinds of ELF thrusters have been developed by MSNW business and Washington University.9 On all of them, the “even-parity” dipole RMF antennas system has been applied. The maximum azimuthal current can up to 20kA with the RF power of RMF.8 The RMF-based thruster has a wide range of power scalability, no magnetic detachment issues, and is essentially propellant independent.6 Therefore, it is thought to one of the most competitive of the high performance electric propulsion system for space. In order to improve the energy confinement and enlarge the local induced azimuthal electric field, an innovation so called “Odd parity” antenna has been applied to the RMF system for FRC.10 The difference between the odd- and even-parity RMF antennas is that the axial variations of Bω. Their symmetric and antisymmetric current drive calculations cases are gained by Guo et. al.11 The FRC current drive experiments has displayed that the FRC thermal confinement will improve evidently if the “Odd parity” antenna is used.12 Comparisons of ion heating by even- and odd-parity RMFs of FRC have been considered by Cohen et. al. using numerical analysis, the results reveal that the ions are better heating in a wider range of odd-parity RMF frequencies.13 The Welch’s PIC simulated results indicate that the good RMF penetration and evolution with odd-parity antenna.14 The investigations of Melnik demonstrate that the odd-parity FRC will make the external magnetic field higher and fluctuations less.15 In a word, the odd-parity RMF antenna is more suitable for the production and confinement of FRC plasma. Therefore, it is feasible to learn the effect of RMF o antenna on the performance of FRC thruster. This paper is arranged into the following sections. The configuration of the antennas will give a brief review in Sec. II. The magnetic field topology will be examined in Sec. III. The simulation results of different RMF antennas are displayed in Sec. IV. Finally, the conclusions are discussed. II. Configuration of the Antennas The schematic of the RMF antenna with even-parity and odd-parity configuration are shown in Fig. 1. 15 Different from the geometric configuration of the current ELE thruster RMF antenna, the antennas are split into two parts so that they can be operated in two differentiated modes. The up and down two

The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8 – 12, 2017

parts of the antennas in Fig. 1 are labeled with blue and red color, respectively. For the even-parity configuration, the currents direction of the up and down antennas are the same. But for the odd-parity configuration, the antennas currents direction of the separated two parts are opposite. Therefore, the horizontal (perpendicular to z direction) magnetic field that created by the RMF antennas are the same as the even-parity case and opposite as the odd-parity case. The pink arrows in Fig. 1 indicate the directions of the induced magnetic field from RMF antennas.

Fig .1 Schematic of two different RMF antennas.15

III. Magnetic Field Topologies of Two RMF antennas For simplicity, a 2D model is established to master the evolution of some parameters. And the numerical results are brought out in section A.

A. Simulation of 2D RMF Current Driven

(a) (b)

Fig. 2 The simulation results of a 2D RMF current driven with COMSOL software. (a) RMF rotation The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8 – 12, 2017

magnetic field; (b) Electron density; (c) Ion density; (d) Current density. A 2D current driven COSMOL fluid model is developed to understand the primary physics process of RMF at first. The simulation results are drawn in Fig. 2. The 2D model consists of four parts. The inner ring is the discharging plasma region. The area between the inner and outer ring is set to the quartz glass. And the eight small rings represent the RMF antennas which carrying sinusoidal currents with phased 900 apart. The rest region is setup to the vacuum. The total input power is 3.5kW, the RMF frequency is 250kHz, and the propellant is Argon. In Fig. 2 (a)-(d) are the numerical results of rotation magnetic field, electron density, ion numerical density, and the driven current, respectively. The maximum rotation magnetic field is 500Gs, the electron density is 3.76e+19m-3, the ion number density is 8.75e+20m-3, and the azimuthal current density is about 5e+3A/m2. The horizontal and the vertical coordinate axis in Fig. 2(a)-(d) represent the x direction and y direction, respectively. And the length units of them are all meter which have not labeled on the figures. Even the numerical results shown in Fig. 2 are a little crude (due to the numerical accuracy), it can provide some quantitative and qualitative references for the further study of the coupling of the RMF and plasma. At first, a significant dynamic rotation magnetic field (as shown in red contour lines) is formed in Fig. 2(a). Then the electron density and ion density will increase as the effect of RMF. The peak density distributions of electron and ion which are as the same shape with RMF are shown in Fig. 2(b) and 2(c). When the electrons are tied to RMF lines and move only along the magnetic field lines, an azimuthal electron current will be occurred and is showed in Fig. 2(d). In order to examine the effect of the RMF frequency on the drive current, the driven electron current density and electron density with different RMF frequencies are plotted in Fig. 3. The range of the frequency is between 150kHz and 300kHz. It is evident that the current density and electron density are direct proportion to the RMF frequency which is agreement with most of the roughly estimated 16,17 result (J휃=neeωr). Besides, there is a turning point on both of the two curves when the RMF frequency is 160kHz. This means that there is a critical optimum frequency for the plasma penetration, ionization, and the current driven of the RMF. That is to say the effect of RMF frequency on the performance of the FRC thruster should be seriously considered.

6 1.4x10 19

4x10

) 2

1.2x106 A/m ( 19

6 3x10 )

1.0x10 3

m ( 5 8.0x10 2x1019

6.0x105 1x1019

4.0x105

Electron density Electron

2.0x105 0

Peak electron current density density current electron Peak Electron current density 0.0 Electron denstiy -1x1019 140 160 180 200 220 240 260 280 300 320 RMF frequency (kHz) Fig. 3 The driven electron current density with different RMF frequencies

B. Magnetic Field Topology of Even- and Odd-parity RMF Antenna Since the 2D model cannot be used to study the coupling of the plasma with different antenna configurations, a 3D COMSOL simulation model is developed. But, the complex and large amount of calculation for the 3D model make it difficult for us to learn the FRC plasma detailed. Thus, some

The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8 – 12, 2017

primary results are given in the following. The 3D model with calculation mesh generation and the cross

Fig. 4 The 3D model with calculation mesh generation and the cross section along z direction section along z direction are shown in Fig. 4. The axial (z) direction cross section magnetic field topologies of the even- and odd-parity RMF antenna are figured in Fig. 5. All parameters in simulations are set to the same as the 2D calculation situation. It is obvious that the intensity of the magnetic field in odd-parity is a little greater. The maximum value of the magnetic field in even-parity is 0.05T, while it is 0.06T in the odd-parity. Meanwhile, the distribution of the magnetic field is more uniform in odd-parity which would be more efficient in the confinement and current drive of the plasma.

Even Odd

Fig. 5 The axial direction cross section magnetic field topology of two different antennas IV. The Simulation Results of Different RMF Antenna The axial direction cross section driven current density with the even- and odd-parity RMF antenna are displayed in Fig. 6. Except the geometry size, the input power, propellant and RMF frequency in the 3D numerical simulation are all set the same as the 2D calculation situation. Similar to the magnetic field topology, the driven azimuthal current density in odd-parity case is more availability than the even-

Even Odd

The 35th International Electric Propulsion Conference, Georgia Institute of Technology, USA October 8 – 12, 2017

Fig. 6 The driven azimuthal current density with different antenna configuration parity antenna. The larger current density in odd-parity RMF antenna shows it can significant improve the performance of the FRC thruster according to the expression of Lorentz Force F=Jθ×Br. In Fig. 7, it shows the axial direction cross section electric field and electron temperature with the even- and odd- parity RMF antenna, respectively. From the simulation results, it easy to see that both of the local electric field and the electron temperature in odd-parity antenna are larger than the even-parity antenna. These results are agreement with those in Ref. 10 and 12. And which can also indicate that the plasma ionization rate and energy confinement will be better. Therefore, the odd-parity antenna may be an effective way to improve the performance of the FRC thruster.

Even Odd

Fig. 7 The axial direction cross section electric field and electron temperature with the even- and odd- parity RMF antenna V. Conclusions The RMF effect on the performance of Field Reversed Configuration Thruster has been studied. It is found that there is a critical optimum frequency for the plasma penetration, ionization, and the current driven of the RMF in 2D model. The 3D simulation results show that the odd-parity RMF antenna is more efficiency than the even-parity antenna in energy confinement, current drive, local electric field, and plasma equilibrium. Thus, the odd-parity may improve the performance of the FRC thruster greatly. Finally, as a result of the complexity and large amount of computations of the 3D model, only the primary results are given in this paper. But, the more simulation and experiment results will be presented later. References

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2J. T. Slough and A. L. Hoffman, “Penetration of a Transverse Magnetic Field by an Accelerated Field-Reversed Configuration,” Physics of Plasma, Vol. 6, No.1, 1999, pp:253-263. 3H. Y. Guo and A. L. Hoffman, “Sustainment of Elongated Field Reversed Configurations with Localized Rotating Magnetic Field Current Drive,” Physics of Plasma, Vol.11, No.3, 2004, pp:1807-1098. 4I. R. Jones, “A Review of Rotating Magnetic Field Current Drive and the Operation of the Rotamak as a Field-Reversed Configuration (Rotamak-FRC) and a Spherical tokamak (Rotamak-ST),” Physics of Plasmas, Vol. 6, No. 5, 1999, pp:1950-1957. 5H. Y. Guo, A. L. Hoffman, and R. D. Milroy, “Rotating Magnetic Field Current Drive of High-Temperature Field Reversed Configuration with High ζ Scaling,” Physics of Plasma, Vol.14, 2007, 112502. 6T. E. Weber, “The Electrodeless Lorentz Force Thruster,” A Ph.D. Dissertation of Washington University, 2006. 7J. T. Slough and K. E. Miller, “Flux Generation and Sustainment of a Field Reversed Configuration with Rotating Magnetic Field Current Drive,” Physics of Plasma, Vol.7, No.5, 2000, pp:1945-1950. 8 Slough and D. Kirtley, “Pulsed Plasmoid Propulsion: The ELF Thruster”, IEPC-2009-265. 9A. P. Pancotti, J. M. Little, J. S. Neuhoff, B. M. Cornella, D. E. kirtley, and J. T. Slough, “Electrodeless Lorentz Force (ELF) Thruster for ISRU and Sample Return Mission,” IEPC-2015-67, 2015, the 34th International Electric Propulsion Conference. 10A. H. Glasser and S. A. Cohen, “Ion and electron acceleration in the Field-Reversed Configuration with an Odd-parity Rotating Magnetic Field,” Physics of Plasma, Vol.9, No.5, 2002, pp:2093-2102. 11H. Y. Guo, A. L. Hoffman, and L. C. Steinhauer, “Observations of Improved Confinement in Field Reversed Configurations Sustained by Antisymmetric Rotating Magnetic Fields,” Physics of Plasmas, Vol.12, 2005, 062507. 12R. D. Milroy, H. Y. Guo, A. L. Hoffman, L. C. Steinhauer, “Antisymmetric RMF Current Drive in FRCs,” Journal of Fusion Energy, Vol. 26, 2006, pp:123-126. 13 S. A. Cohen, A. S. Landsman, and A. H. Glasser, “Stochastic Ion Heating in a Field-Reversed Configuration Geometry by Rotating Magnetic Fields,” Physics of Plasma, Vol.14, 2007, 072508. 14 D. R. Welch, T. C. Genoni, S. A. Cohen, and A. H. Glasser, “Particle-in-Cell Modeling of Field Reversed Configuration Formation by Odd-parity Rotation Magnetic Fields,” Journal of Fusion Energy, Vol. 29, 2010, pp:584-587. 15P. Melnik, “Convective Power Loss Measurement in a Field Reversed Configuration with Rotating Magnetic Field Current Drive,” A Ph.D. Dissertation of Washington University, 2014. 16M. Ohnishi, T. Chikano, M. Tsukamoto, M. Fukuhara, T. Masaki, H. Osawa, and W. Hugrass, “Formation of Field-Reversed Configuration by Larger Rotating Magnetic Field,” J. Plasma Fusion Res. SERIES, Vol.8, 2009, pp:1062-1065. 17T. Motomura, S. Shinohara, T. Tanikawa, T. Hada, I. Funaki, H. Nishida, K. P. Shamrai, T. Matsuoka, F. Otsuka, T. S. Rudenko, E. Ohnl, K. Yokoi, and T. Nakamura, “Development of Electrodeless Electric Propulsion Systems Using High-Density Helicon Plasmas: The HEAT Project,” 2011, The URSI General Assembly and Scientific Symposium, Istanbul, Turkey.

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