Suppression of the Biermann Battery and Stabilization of the Thermomagnetic Instability in Laser Fusion Conditions

Abstract

Magnetic field generated by the Biermann battery is thought to be one of the principal mechanisms behind inhibition of heat-flow in laser-plasma interactions, and is predicted to grow exponentially in some contexts due to the thermomagnetic instability [Tidman & Shanny, Phys. Fluids 17 (1974)]. In contrast to these predictions, however, we have conducted Vlasov-Fokker-Planck simulations of magnetic field dynamics under a range of classically unstable laser-fusion conditions, and find field generation to be strongly suppressed, preventing magnetization of the transport, and stabilizing instability. By deriving new scaling laws, we show that this stabilization is a consequence of: (i) heavy suppression of the Biermann battery under non-local conditions; (ii) rapid convection of magnetic field by the heat-flow; and (iii) comparatively short field length-scales. Our results indicate that classical models substantially overestimate the importance of magnetic fields generated by the Biermann battery, and the susceptibility of laser-fusion plasmas to the thermomagnetic instability.

Effects of collisions on the generation and suppression of temperature anisotropies and the Weibel instability

“…We do not observe the thermomagnetic instability, confirming Ref. [23], but we also do not observe any of the predicted reduction of the Biermann battery growth. This is likely because we start from a Maxwellian distribution where the Biermann battery should grow rather than evolve to a such a state by plasma heating and expansion.…”

“…However, Ref. [23] showed that this instability is suppressed due to the Nernst effect and that the growth of the Biermann battery is reduced. The Nernst effect, when only the most energetic electrons are frozen into the magnetic field, is expected to drag Biermann generated fields in the direction of heat flux allowing them to pile up [24][25][26][27][28][29][30].…”

Instability in a magnetised collisional plasma driven by a heat flow or a current

“…A number of plasma instabilities are known to be associated with strong heat flow in laser-plasmas. These include the Tidman & Shanny instability (Tidman & Shanny 1974, Sherlock & Bissell 2020, the Weibel instability (1959), the electrothermal instability (Haines 1981), the ion-acoustic instability that generates an anomalous resistivity (Forslund 1970, Rozmus et al 2018, and the field-compressing magnetothermal instability of Bissell et al (2010). Apart from the fieldcompressing magnetothermal instability these instabilities do not require a pre-existing zeroth order magnetic field.…”

Magnetic Signatures of Radiation-Driven Double Ablation Fronts

“…These discrepancies are likely due to nonequilibrium effects on the radiation transport and kinetic effects, such as nonlocal transport, that are not included in the model. For example, recent work using kinetic simulations has demonstrated that MHD models overestimate the rate of Biermann battery field generation in plasmas with long electron mean free paths [37,38]. In this case, artificially enhanced field strengths would result in overfocusing of the protons to produce features at narrower radii.…”

“…Estimates based on Ref. [37] suggest a suppression of the Biermann battery generation rate by factors ranging from ∼0.2 to 0.5 across the plume (additional details about this calculation, including comparisons with experimental results, can be found in the Supplemental Material [39]). These experimental results could be used to verify kinetic predictions of Biermann battery suppression.…”