V = 1 / n , the specific volume.

b) viscid case

to allow long term simulations: inclusion of an ion viscosity term

accounting for anomalous plasma transport

(keywords: plasma turbulence due to multiple ion streaming after the

collapse event, coarse-grained ion Vlasov distribution function)

~ supersonic propagation of a

peaked ion density front, the peak

being a remnant of the density collapse [2,3]

~ essentially 3 phases of evolution can be distinguished :

i) initial phase up to ion density bunching

ii) a stable peaked ion density front propagating with constant

velocity supersonically towards vacuum

iii) decay of the leading density hump due to debunching and

further acceleration of the resultant tiny ion front up to a

value determined by self-similar theory [2,3]

NUMERICAL SUBTLETIES :

~ exact numerical treatment of ion dynamics by a Lagrangian code [1,2]

~ need for a Poisson solver of high resolution and fast convergence of

the iteration procedure [1,2]

~ tri-diagonal coefficient matrix for the discretized evolution equations

with open (i.e. differential) boundary conditions [1,2]