A non-relativistic model of plasma physics containing a radiation reaction term

Abstract

While a fully relativistic collisionless plasma is modeled by the Vlasov-Maxwell system a good approximation in the non-relativistic limit is given by the Vlasov-Poisson system. We modify the Vlasov-Poisson system so that damping due to the relativistic effect of radiation reaction is included. We prove the existence and uniqueness as well as the higher regularity of local classical solutions. These theorems also include the higher regularity of classical solutions of the Vlasov-Poisson system depending on the regularity of the initial datum.Date: March 2016. 1991 Mathematics Subject Classification. 35B30 / 35L60 / 78A40 / 82C21 / 82C22 / 82D10.

Microscopic Foundations of Kinetic Plasma Theory: The Relativistic Vlasov–Maxwell Equations and Their Radiation-Reaction-Corrected Generalization

“…Radiation-reaction corrections to the Vlasov-Maxwell system, based on the works of Dirac [Dir38] and Landau-Lifshitz [LaLi51], have been proposed in [HaMa68,Hak11], [Kuz78] and [NoBu13], and an H-theorem proved for them in [HaMa68] and [BuNo14]. For mathematically rigorous studies of a radiation-reaction corrected Vlasov-Poisson system, see [KuRe01a,KuRe01b] and [Bau18], and also references therein.…”

On global solutions to the Vlasov-Poisson system with radiation damping

“…Actually, effect of radiation damping should is characterized by the second derivativeD(t) = D [2] (t) + ε ... D(t) (ρ + + ρ − )dx of the dipole moment D(t) = R 3 xρ(t, x)dx. Nevertheless, the corresponding mathematical model becomes more intricate and there has been no any progress up to now (see [21,4] for detailed discussion). For another simplified model proposed in [4] which is slightly more complex than (1), S. Bauer established local existence of classical solutions for general smooth initial data f ± 0 (x, v), at present existence and asymptotic behavior of global classical solutions are obtained only for small initial data [7].…”

“…and |D [2] (t)| ≤ C(1 + t) −8/7 , t > 0, (4) where C is a positive constant depending only upon the initial data.…”