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