Abstract
The acceleration of a onedimensional uniform plasma slab is analyzed using fully electromagnetic particleincell simulations. Two different regimes of ion dynamics are observed. At relatively high magnetic field values, the ions are accelerated nearly ballistically in a thin sheath at the plasmavacuum interface and then form a beam which propagates through the downstream bulk plasma. This behavior can be explained by a simple collisionless thinsheath model. At lower field values the sheath becomes thicker and the ions are collisional at the interface. This leads to “snowplowing” of ion density at the interface. From the electron transport equations for a simple magnetized plasma we can estimate the temperature and effective collisionality in the sheath as a function of magnetic field strength. From this theory we can qualitatively explain the existence of the two regimes. In the simulations the plasma sheath thickness is found to scale somewhat more weakly with magnetic field strength than is predicted by the simple transport theory. We propose that a high Mach numberplasma slab may be obtained by the combination of a short accelerator and a strong magnetic field in the collisionless regime.
This work was supported by the U.S. Department of Energy (DOE), Office of Fusion Energy Science (OFES), under Grant No. DEFG0205ER54835. The authors worked under subcontract H008 of HyperV Technologies Corporation of Chantilly, Virginia. We gratefully acknowledge helpful conversations with Dr. Doug Witherspoon of HyperV, Dr. JinSoo Kim and Dr. Nick Bogatu of FarTech, and Dr. Joseph MacFarlane and Dr. Igor Golovkin of Prism Computational Sciences. We also thank Dr. David Rose of Voss Scientific LLC for careful review of this manuscript and many helpful suggestions.
I. INTRODUCTION
II. ELECTRON AND ION DYNAMICS: “BALLISTIC” REGIME
III. COLLISIONLESS ION (THINSHEATH) MODEL
IV. ELECTRON AND ION DYNAMICS: SNOWPLOW REGIME
V. THEORY AND SIMULATION OF SHEATH THICKNESS
VI. DISCUSSION AND CONCLUSIONS
Key Topics
 Plasma sheaths
 91.0
 Magnetic fields
 32.0
 Trajectory models
 18.0
 Plasma dynamics
 15.0
 Plasma temperature
 13.0
Figures
Coaxial plasma jet accelerator (adapted from Ref. 2). The plasma jet originates at the left and accelerates axially to the right due to the force.
Coaxial plasma jet accelerator (adapted from Ref. 2). The plasma jet originates at the left and accelerates axially to the right due to the force.
Schematic figure of 1D Cartesian plasma jet simulation. The magnetic field on the left diffuses into the conductive plasma which is accelerated to the right by the resulting force. In the 1D geometry the direction corresponds to the axial direction in Fig. 1.
Schematic figure of 1D Cartesian plasma jet simulation. The magnetic field on the left diffuses into the conductive plasma which is accelerated to the right by the resulting force. In the 1D geometry the direction corresponds to the axial direction in Fig. 1.
Snapshots (at ) of (a) , and (b) ion, and (c) electron phasespace particle densities for 1D kinetic plasma jet simulation A (see Table I for parameters).
Snapshots (at ) of (a) , and (b) ion, and (c) electron phasespace particle densities for 1D kinetic plasma jet simulation A (see Table I for parameters).
Average ion axial velocity as a function of time for simulation A.
Average ion axial velocity as a function of time for simulation A.
Snapshots of ion particle phasespace charge density at (a) , (b) 25, (c) 50, and (d) 75 ns for simulation A. The contour levels are the same, as shown in Fig. 3.
Snapshots of ion particle phasespace charge density at (a) , (b) 25, (c) 50, and (d) 75 ns for simulation A. The contour levels are the same, as shown in Fig. 3.
Snapshots of ion particle phasespace charge density at (a) , (b) 125, (c) 150, and (d) 175 ns for simulation A. The contour levels are the same, as shown in Fig. 3.
Snapshots of ion particle phasespace charge density at (a) , (b) 125, (c) 150, and (d) 175 ns for simulation A. The contour levels are the same, as shown in Fig. 3.
Snapshot of magnetic field profile at for simulation A.
Snapshot of magnetic field profile at for simulation A.
Sheath edge and mean plasma position as a function of time for simulation A. The coordinate system in this plot has been adjusted so that .
Sheath edge and mean plasma position as a function of time for simulation A. The coordinate system in this plot has been adjusted so that .
Schematic of idealized ion phasespace data. The velocity scale and time scales are defined in the text.
Schematic of idealized ion phasespace data. The velocity scale and time scales are defined in the text.
Schematic of the “cycle” of idealized ion phasespace data .
Schematic of the “cycle” of idealized ion phasespace data .
Idealized ion dynamics model results showing , , and as functions of time.
Idealized ion dynamics model results showing , , and as functions of time.
Sheath position as a function of time for simulations with varying values of . Simulation parameters are given in Table I.
Sheath position as a function of time for simulations with varying values of . Simulation parameters are given in Table I.
Snapshots (at ) of (a) , and (b) ion and (c) electron phasespace particle densities for 1D kinetic plasma jet simulation B (see Table I for parameters).
Snapshots (at ) of (a) , and (b) ion and (c) electron phasespace particle densities for 1D kinetic plasma jet simulation B (see Table I for parameters).
Detailed view in the sheath region of normalized ion mean velocity and magnetic field at for simulation A.
Detailed view in the sheath region of normalized ion mean velocity and magnetic field at for simulation A.
Calculated sheath thickness as a function of time for simulations with varying values of . Simulation parameters are given in Table I. Note that simulations A and F have the same value of , but differing values for the linear ramp duration on the input power.
Calculated sheath thickness as a function of time for simulations with varying values of . Simulation parameters are given in Table I. Note that simulations A and F have the same value of , but differing values for the linear ramp duration on the input power.
Tables
Parameters used in 1D plasma jet simulations. For all simulations the initial ion and electron temperature are 5 eV. is the vacuum field value, and is the initial (uniform) plasma number density. The Alfvén velocity is calculated from and using Eq. (2).
Parameters used in 1D plasma jet simulations. For all simulations the initial ion and electron temperature are 5 eV. is the vacuum field value, and is the initial (uniform) plasma number density. The Alfvén velocity is calculated from and using Eq. (2).
Theory results from input parameters of 1D plasma jet simulations. Ion phasespace data from simulation A is shown in Fig. 3. Results from simulation B are shown in Fig. 13.
Theory results from input parameters of 1D plasma jet simulations. Ion phasespace data from simulation A is shown in Fig. 3. Results from simulation B are shown in Fig. 13.
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