University of Nevada, Reno
Collisionless Plasma Flow in External Magnetic Field
Plasmafully ionized hydrogenplasma length : 4 mmcollision frequency : νce = 2x 108 1/sec
flow velocity usw=4x107 cm/s
External Magnetic Fieldprofile : electron gyrofrequency : ωce = 1.76 x 1011 rad/sec @ B =
10 kGelectron gyroradius : re = 16 μm @ B = 10 kG
ion gyroradius : ri = usw/ωci = 0.42cm @ B = 10 kG
Bex0 /(1cm x);7kG@x 0 65kG@x 1cm
Bex0 /(1cm x);7kG@x 0 65kG@x 1cm
Computational Parametermesh size : Δx = 1.426 μmtime step : Δt = 4.65 fstotal simulation time : 20 ns
1D-PIC SIMULATION PARAMETER
x D re ri
x D re ri
t 1/ pe 1/ ce 1/ ci ~1ns < 20ns
t 1/ pe 1/ ce 1/ ci ~1ns < 20ns
TIME EVOLUTION OF ION DENSITY
MAGNETIC FIELD IS PARTIALLY NEUTRALIZED BY SELF-INDUCED FIELD
Negative B-field is excited by electrons circular motion at the plasma expansion front.
NEGATIVE ELECTROSTATIC FIELD IS EXCITED AT PLASMA FRONT
Ion Expansion Front
Since electrons are magnetized, ions go ahead and make a negative sheath field at the plasma
front.
Figure : Electron phase plot X-px (left) & X-py (right) at t=9.3ns
ELECTRONS ARE ACCELERATED BY NEGATIVE SHEATH FIELD AND DO CIRCULAR MOTION
Figure : Ion phase plot X-Px at 4.6 ns (left) and 9.3 ns (right).
IONS ARE DECELERATED BY NEGATIVE SHEATH FIELD
Figure : Energy spectrum at t=9.3ns.
Te~1.2keV (Initial Te ~ 400eV)
ENERGY SPECTRA SHOW IONS LOSE ENERGY AND ELECTRONS ARE HEATED
~ Flow velocity
Low energy ions increases.
Ex u ec
Bnet
Ex u ec
Bnet
i ~ eExs
i ~ eExs
Ions are stopped when they transfer half of their own energy to the electrons
i eu ec
Bnet re
eu ec
Bnet p ec
eBnet
u e p e ~ 2e
i eu ec
Bnet re
eu ec
Bnet p ec
eBnet
u e p e ~ 2e
SUMMARY OF WHAT’S GOING ON
(Assumed the effective collision frequency is the electron cyclotron frequency )
(Assumed the ion energy equals to the sheath potential )
Y. Sentoku, K. Mima, P. Kaw, and K. Nishikawa, Phys. Rev. Lett. 90 (2003) 155001
IONS START FLOWING BACKWARD AFTER 10 NSEC
ne=2x1016 ccm
Te=5keV
usw=8x108 (0.0267c)
Plasma = 1.8mm x 0.72mm
External B-field (Z-direction)100kG@x=0 - 500kG@x=5.4mmωce=1.8x1012 rad/sec @B=100kG
re=20μm@B=100kG
Δx=3.6μmLx=7.1mm, Ly=1.8mm
2D-PIC PARAMETERS
Density is normalized by n0=2x1016 ccm
200kG
t=120 ps
t=360 ps
t=240 ps
TIME EVOLUTION OF ION DENSITY
TIME EVOLUTION OF ELECTRON DENSITY
t=120 ps
t=360 ps
t=240 ps
Ex @ t=60ps
Ey @ t=60ps
Bz @ t=60ps
FIELD STRUCTURE AT T=60ps
Bz = 0.0002~20kG
Ex = 0.0002~5.8 V/m
FIELD STRUCTURE AT T=175ps
Ex @ t=175ps
Ey @ t=175ps
Bz @ t=175ps
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