Computer Modeling Of Plasma Focus Discharges

Computer modeling of plasma focus discharges V.V.Vikhrev RRC Kurchatov Institute, Moscow, Russia

Three models are constructed for description of plasma focus dynamics: 1) two-dimensional snow-plough model, 2) two-dimensional MHD model of fully ionized plasma 3) One-dimensional three-fluids MHD-model.

 2I  H e cR

Two dimensional snow-plough model

H2 pmf  8  H2  f  2 R l n 8

M R  cm R Vn  t 

Using snow-plough model for Mather type plasma focus..

Using snow-plough model for Filippov type plasma focus..

Circuit t

d 1 ( LI )  R0 I  U Ñ  U 0   I dt dt C0 L – inductance, C –capacity, R0 – resistance of the circuit, I – current, U0 – initial voltage,  dL 1 R   Vn d dt R 

Two-dimensional MНD model of fully ionized plasma Is used fully ionised hydrogen plasma under the assumption of axially symmetric discharge development.

n  div(nV )  0 t

B  rot[V  B]  0 t

 nV 2 1  div(nV V )   grad (nT )  [rotB  B] t mi 4 mi

3   nT   div(nTV )   nTdiv(V )  2 t 

n is the plasma density, T is temperature V is the hydrodynamic velocity, B is the magnetic field strength, mi is mass of ions

Using 2-D MHD for Mather type plasma focus

Using 2-D MHD for Mather type plasma focus

Using 2-D MHD for Mather type plasma focus

One-dimensional three-fluids MHD-model • Is consider plasma from atoms, electrons and ions • ne = ni = n • Ti = Ta = T • Ver = Vi

Equation for electron temperature of plasma

Equation for ions and atoms temperature of plasma

Comperision with experiment

Comperision with expeiment, p=0.2 torr

Comperision with experiment, p=0.6 torr

Comperision with experiment, p=1 torr

Conclusions – Snow-plough model and 2D MHD model predicts current shape in time and current sheath motion. Results of simulation are well matched with experimental results. – 3 fluid model predicts the amount of gas, which is not captured by current sheath, leakage of current near isolator. Analysis has shown a good coincidence of numerical results with magnetic probe measurements. Model predicts that almost all the current flows within the current sheath.