On the limitations of gyrokinetics: Magnetic moment conservation

Stephens, C. D.; Brzozowski, Robert W.; Jenko, F.

doi:10.1063/1.4998968

Cited by 6 publications

(6 citation statements)

References 28 publications

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“…After the loss cone size is determined, we set initial distributions of particle velocities in the velocity space: 372 points evenly distributed in v ⊥1 , v ⊥2 plane inside the loss cone (see Figure 6). It should be noted that the magnetic moment conserves only in the frame moving with the guiding center (Stephens et al., 2017). The guiding center drift velocity is negligible at the ionospheric altitude but it cannot be neglected at r = 3.5 R E .…”

Section: Methodsmentioning

confidence: 99%

Conditions of Loss Cone Filling by Scattering on the Curved Field Lines for 30 keV Protons During Geomagnetic Storm as Inferred From Numerical Trajectory Tracing

et al. 2020

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The rate of pitch angle scattering on the curved magnetic field lines is well parameterized by the ratio of the minimum field line curvature radius to the maximum effective particle gyroradius (K = RC/rg). The critical value of this ratio (Kcr) corresponding to the loss cone filling is of special interest since it corresponds to the low altitude isotropic boundaries (IBs). The early theoretical estimates gave Kcr = 8, whereas recent estimations of the K parameter on the field lines corresponding to the observed IBs during the geomagnetic storms revealed KIB values in the range of 3–30. We numerically trace the trajectories of the 30 keV protons in the magnetic field of the global magnetohydrodynamic simulation of the intense storm in order to infer statistical distribution of Kcr. The electric field and effects of nonstationarity are neglected in this study. It is found that although the Kcr values do show some variations during the course of the storm, its range is rather narrow 4 < Kcr < 8. The result suggests that higher KIB values found in the observational studies, if not caused by the magnetosphere‐ionosphere mapping error, should be attributed to some other mechanism of pitch angle scattering. The Kcr values tend to be lower (4–6) during the main phase because the region of low K values approaches the Earth and the equatorial loss cone size becomes larger due to a larger equatorial magnetic field in the near‐earth region. The remaining variation of Kcr is explained by the presence of the guide component of the magnetic field.

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Section: Methodsmentioning

confidence: 99%

Conditions of Loss Cone Filling by Scattering on the Curved Field Lines for 30 keV Protons During Geomagnetic Storm as Inferred From Numerical Trajectory Tracing

et al. 2020

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“…Under such conditions, the magnetic moment is adiabatically conserved (Brizard & Hahm 2007; Stephens et al. 2017), and the gyromotion can be decoupled from the guiding centre motion: where is equivalent to the gyrophase, is the gyroradius and the subscript ‘’ refers to the location of the particle's guiding centre. These guiding centre variables obey the guiding centre equations of motion.…”

Section: Action-angle Variablesmentioning

confidence: 99%

“…Essentially, we apply gyrokinetics to situations where we can decouple the fast gyromotion of the charged particle from the slow drift motion; this can be done when the time scale of the gyromotion is significantly faster than all other time scales in the system and when the gyroradius is smaller than almost all other length scales in the system. In such a scenario, the magnetic moment is conserved, leading to a significant reduction in the complexity of the dynamics (Stephens, Brzozowski III & Jenko 2017). Moreover, gyrokinetics incorporates an ordering where the modes are anisotropic and flute-like, meaning that the characteristic parallel wavelength of the mode is large but perpendicular wavelengths can be comparable to the gyroradius.…”

Section: Introductionmentioning

confidence: 99%

Quasilinear gyrokinetic theory: a derivation of QuaLiKiz

et al. 2021

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In order to predict and analyse turbulent transport in tokamaks, it is important to model transport that arises from microinstabilities. For this task, quasilinear codes have been developed that seek to calculate particle, angular momentum and heat fluxes, both quickly and accurately. In this tutorial, we present a derivation of one such code known as QuaLiKiz, a quasilinear gyrokinetic transport code. The goal of this derivation is to provide a self-contained and complete description of the underlying physics and mathematics of QuaLiKiz from first principles. This work serves both as a comprehensive overview of QuaLiKiz specifically as well as an illustration for deriving quasilinear models in general.

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“…The guiding center approximation used in this work is justified by the adiabatic conservation of the magnetic moment, which requires that the gyroradius be small compared to other relevant length scales in the system. [32][33][34][35][36] We impose two conditions on the guiding center particle orbit to determine the bounce-transit motion to lowest-order in the gyroradius:…”

Section: Circular Magnetic Geometrymentioning

confidence: 99%