Plasma Expansion into a Vacuum

Abstract

The charge separation effects in the collisionless plasma expansion into a vacuum are studied in great detail. Accurate results are obtained concerning the structure of the ion front, the resultant ion energy spectrum, and more specifically the maximum ion energy. These are of crucial importance for the interpretation of recent experiments, where high-energy ion jets were produced from short pulse interaction with solid targets.

Investigations of Field Dynamics in Laser Plasmas with Proton Imaging

“…Apart from the electric field which peaks at the ion front E F ront , the electric field between target surface and the front is almost homogeneous and decreases with E P lateau ∝ t −2 [46,47].…”

“…The self-similar solution is not valid for ω pi t < 1 when the initial Debye length is larger than the self-similar scale length c s t. Also for ω pi t ≫ 1 the ion velocity would increase unlimited for x → ∞. The self-similar solution becomes invalid when the Debye length equals the density scale length c s t, this position corresponds to the ion front [47]:…”

“…To describe the electric fields for all times and the temporal evolution of the densities also for x < 0, numerical methods have to be applied. In [46,47] an expression for the field at the front has been found: 30) with τ F = ω pi t/ √ 2e E . For t = 0 and ω pi ≫ 1 this expression is similar to the formulas discussed above (see also [45]).…”

“…This can be integrated analytically for x = 0 to x = ∞ and delivers the initial electric field at x = 0 [47]: 20) where E i = n e0 k B T e /ε 0 and e E = 2.71828... . This initial electric field depends on the initial electron density n e0 and the electron temperature T e only.…”

“…For an initial electron density of n e0 = 5 · 10 20 cm −3 and a temperature of T e = 600 keV the electric field is about 2 · 10 12 V/m (see also Chapter 3). The temporal evolution of the ion and electron densities is described by the equations of continuity and motion [47]: 22) where v i is the ion velocity and m i the ion mass. For x + c s t > 0, with the ion-acoustic velocity c s = Zk B T e /m i , a self-similar solution exist, if quasi-neutrality in the expanding plasma, n e = Zn i = n e0 exp (−x/c s t − 1) is assumed.…”