Electron cyclotron resonant heating: A simpler method for deriving the linear wave equations in a nonuniform magnetic field

1994 ◽  
Vol 1 (4) ◽  
pp. 842-849 ◽  
Author(s):  
D. C. McDonald ◽  
R. A. Cairns ◽  
C. N. Lashmore‐Davies
Keyword(s):  
Magnetic Field ◽  
Wave Equations ◽  
Electron Cyclotron ◽  
Nonuniform Magnetic Field ◽  
Linear Wave ◽  
Linear Wave Equations ◽  
Resonant Heating ◽  
Simpler Method

Linearized expressions for perturbed quantities for propagation at arbitrary angle to the static magnetic field in plasmas with non-uniform density and thermal anisotropy

1978 ◽  
Vol 20 (2) ◽  
pp. 171-181 ◽  
Author(s):  
R. Koch
Keyword(s):  
Magnetic Field ◽  
Static Magnetic Field ◽  
Wave Equations ◽  
Operator Method ◽  
Equilibrium Density ◽  
Uniform Density ◽  
Linear Wave ◽  
Thermal Anisotropy ◽  
Maxwellian Plasma ◽  
Linear Wave Equations

This paper is concerned with the derivation of linear wave equations for nonuniform magnetized Vlasov plasmas. By the operator method it is shown that a close connection exists between the case of perpendicular propagation and the general one. Combining this with previous results, expressions for the perturbed density and velocity are derived for the case of propagation at any angle to the uniform static magnetic field in a two-temperature Maxwellian plasma. These results apply for arbitrary inhomogeneities of equilibrium density and temperatures in directions perpendicular to the static magnetic field.

Uniqueness for stochastic non-linear wave equations

2007 ◽  
Vol 67 (12) ◽  
pp. 3287-3310 ◽  
Author(s):  
Martin Ondreját
Keyword(s):  
Wave Equations ◽  
Linear Wave ◽  
Non Linear ◽  
Linear Wave Equations

An inverse scattering theorem for (1 + 1)-dimensional semi-linear wave equations with null conditions

2021 ◽  
Vol 18 (01) ◽  
pp. 143-167
Author(s):  
Mengni Li
Keyword(s):  
Inverse Scattering ◽  
Wave Equations ◽  
Scattering Problem ◽  
Weighted Sobolev Spaces ◽  
One Dimension ◽  
Energy Estimates ◽  
Small Data ◽  
Linear Wave ◽  
Global Existence Of Solutions ◽  
Linear Wave Equations

We are interested in the inverse scattering problem for semi-linear wave equations in one dimension. Assuming null conditions, we prove that small data lead to global existence of solutions to [Formula: see text]-dimensional semi-linear wave equations. This result allows us to construct the scattering fields and their corresponding weighted Sobolev spaces at the infinities. Finally, we prove that the scattering operator not only describes the scattering behavior of the solution but also uniquely determines the solution. The key ingredient of our proof is the same strategy proposed by Le Floch and LeFloch [On the global evolution of self-gravitating matter. Nonlinear interactions in Gowdy symmetry, Arch. Ration. Mech. Anal. 233 (2019) 45–86] as well as Luli et al. [On one-dimension semi-linear wave equations with null conditions, Adv. Math. 329 (2018) 174–188] to make full use of the null structure and the weighted energy estimates.

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