Electron temperature anisotropy instabilities represented by superposition of streams

Abstract

The generation of magnetic field, together with the electrostatic activity met in the saturation regime of the Weibel instability (WI), is investigated by means of an analytical multi-stream model in a Hamiltonian framework. Taking advantage from the invariance of the generalized canonical momentum, the model allows to reduce the full kinetic 1D2V Vlasov equation into several 1D1V equations while keeping its kinetic character. The multi-stream model provides a more complete and accurate picture of the Weibel instability, because it is possible to separate the specific contribution of each stream during the development of the Weibel instability. An interesting result for the multi-stream mode is a lower cost in the perpendicular treatment of the py momentum component since no differential operator associated with some approximate numerical scheme has to be carried out on this variable. Indeed, a small number of streams or particle classes are sufficient to correctly describe the magnetic field generation and the mixed electrostatic- electromagnetic nature of the instabilit

Conditions for the onset of the current filamentation instability in the laboratory

“…The blue curve shows the growth of magnetic field energy generated by the fireball beam with energy spread ∆p x /γ b = 0.29, while the red curve is associated with the lower energy spread ∆p x /γ b = 0.13. Simulation results demonstrate that the CFI grows in all cases, in agreement with analytical calculations (Inglebert & Ghizzo 2012). The green line in Fig.…”

On the multistream approach of relativistic Weibel instability. III. Comparison with full-kinetic Vlasov simulations

“…7 and 8 or within the framework of the multistream model in Ref. 9 in the non relativistic regime of WI. However, the existing kinetic codes (both PIC and Vlasov) cannot account for effects caused by trapped particle populations of very low densities.…”

Fluid description of Weibel-type instabilities via full pressure tensor dynamics

“…This has no counterpart in the full kinetic treatment and is similar to the A > 1 condition for WI case (first of eqs. (19)). It can be qualitatively understood along the lines of the "pure WI" limit of the coupled WI-CFI mode, by noting that for |u 0 | ∼ c s the beam velocity distributions in the phase-space tend to overlap ( fig.…”

“…However, some of the conclusions drawn within these cold models, such as the complete de-coupling between the CFI purely electromagnetic (e.m.) and electrostatic features [10] in some limits, have proven not to survive in a full kinetic treatment with non-null beam temperatures [11][12][13]. Kinetic features have been instead successfully described by means of kinetic reduced models based on specific classes of electron distribution functions, such as waterbags [14][15][16][17], multi-stream distributions [18], combinations of the two [19] or some of their special cases, such as "multi-ring" distributions [20][21][22]. While on the one hand such special classes of particle distributions 45001-p1 are useful both for the numerical initialisation of these instabilities, especially in the relativistic regime, and for their numerical simulation at a lower computational cost, on the other hand the exact analytical calculations they typically allow provide a valuable insight into the physics of Weibel-type modes.…”

“…While on the one hand such special classes of particle distributions 45001-p1 are useful both for the numerical initialisation of these instabilities, especially in the relativistic regime, and for their numerical simulation at a lower computational cost, on the other hand the exact analytical calculations they typically allow provide a valuable insight into the physics of Weibel-type modes. The multi-stream description, for example, has provided a unifying framework for the description of both pure WI and CFI, by highlighting the representability of a temperature anisotropy as a momentum anisotropy [18,19].…”