Non-linear coupling in a magnetized plasma

Sjolund, A.; Stenflo, L.

doi:10.1007/bf01326195

Cited by 43 publications

(13 citation statements)

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“…Having expressed other first order perturbations in terms of E 1 , the electric field equation (18) constrains the relations between the wave amplitude E (1) k , the wave frequency ω k , and the wave vector k. Substituting the expression (16) for v s1 into the electric field equation, we obtain the first order electric field equation in the momentum space…”

Section: A First Order Equationsmentioning

confidence: 99%

Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian

2017

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Large amplitude waves in magnetized plasmas, generated either by external pumps or internal instabilities, can scatter via three-wave interactions. While three-wave scattering is well known in collimated geometry, what happens when waves propagate at angles with one another in magnetized plasmas remains largely unknown, mainly due to the analytical difficulty of this problem. In this paper, we overcome this analytical difficulty and find a convenient formula for three-wave coupling coefficient in cold, uniform, magnetized, and collisionless plasmas in the most general geometry. This is achieved by systematically solving the fluid-Maxwell model to second order using a multiscale perturbative expansion. The general formula for the coupling coefficient becomes transparent when we reformulate it as the scattering matrix element of a quantized Lagrangian. Using the quantized Lagrangian, it is possible to bypass the perturbative solution and directly obtain the nonlinear coupling coefficient from the linear response of the plasma. To illustrate how to evaluate the cold coupling coefficient, we give a set of examples where the participating waves are either quasitransverse or quasilongitudinal. In these examples, we determine the angular dependence of three-wave scattering, and demonstrate that backscattering is not necessarily the strongest scattering channel in magnetized plasmas, in contrast to what happens in unmagnetized plasmas. Our approach gives a more complete picture, beyond the simple collimated geometry, of how injected waves can decay in magnetic confinement devices, as well as how lasers can be scattered in magnetized plasma targets.

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Section: A First Order Equationsmentioning

confidence: 99%

Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian

2017

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“…To convert the above symbolic expressions to actual solutions, we need to find an explicit expression for the warm forcing operator. Using the momentum equation, the warm forcing operator satisfieŝ (27) for any Z ∈ C 3 . In the above equation, β s,k = Ω s /ω k is the magnetization ratio, where Ω s = e s B 0 /m s is the gyrofrequency; b is the unit vector along B 0 ; and u 2 s := ε s /m s = ξ s k B T s0 /m s is the thermal speed.…”

Section: A First-order Equationsmentioning

confidence: 99%

“…, it is a straightforward calculation to verify thatF given by the above formulas satisfies Eq. (27). The warm forcing operator inherits a number of properties from F and P. First, since F † = F is self-adjoint with respect to vector inner products, the warm forcing operatorF † =F is also self-adjoint, although P † = P is not.…”

Section: A First-order Equationsmentioning

confidence: 99%

Three-wave interactions in magnetized warm-fluid plasmas: General theory with evaluable coupling coefficient

Shi

2019

Phys. Rev. E

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Resonant three-wave coupling is an important mechanism via which waves interact in a nonlinear medium. When the medium is a magnetized warm-fluid plasma, a previously-unknown formula for the coupling coefficients is derived by solving the fluid-Maxwell's equations to second order using multiscale perturbative expansions. The formula is not only general but also evaluable, whereby numerical values of the coupling coefficient can be determined for any three resonantly interacting waves propagating at arbitrary angles. As one example, coupling coefficient governing laser scattering is evaluated. In conditions relevant to magnetized inertial confinement fusion experiments, lasers scatter from magnetized plasma waves and the growth rates are modified at oblique angles. As another example, coupling coefficient between two Alfvén waves via a sound wave is evaluated. In conditions relevant to solar corona, the decay of a parallel Alfvén wave only slightly prefers exact backward geometry.

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“…Refs. [13,29,33,37]. Of special interest here is the three wave interaction processes, that have a wide range of applications, including e.g.…”

Section: Introductionmentioning

confidence: 99%

Three-wave interaction and Manley–Rowe relations in quantum hydrodynamics

2014

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Non-linear coupling in a magnetized plasma

Cited by 43 publications

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Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian

Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian

Three-wave interactions in magnetized warm-fluid plasmas: General theory with evaluable coupling coefficient

Three-wave interaction and Manley–Rowe relations in quantum hydrodynamics

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