Ballooning modes and their stability in a near-Earth plasma

Mazur, N. G.; Fedorov, E. N.; Pilipenko, Vyacheslav

doi:10.5047/eps.2012.07.006

Cited by 21 publications

(33 citation statements)

References 23 publications

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“…The wave's two‐dimensional electric field

{\overset{E}{true}}_{⊥}

can be represented as the sum of potential and vortical components. In the small azimuthal scale limit, the latter is k ∥ / k ⊥ times smaller than the former and can be neglected [e.g., Klimushkin , ; Mazur et al , ]. Then, the wave's electric field can be represented as

{\overset{E}{true}}_{⊥} = - \nabla_{⊥} ψ .

…”

Section: Mhd Approachmentioning

confidence: 99%

“…is responsible for the Alfvén and slow mode coupling. For details of the system ( and ) derivation, see Klimushkin [] and Mazur et al []. The dispersion relation which follows from this system is written as

((), ω^{2} - k_{∥}^{2} v_{A}^{2} - \frac{k_{y}^{2}}{k_{⊥}^{2}} \frac{2 P^{'}}{ρR}) ((), ω^{2} - k_{∥}^{2} v_{s}^{2}) = \frac{k_{y}^{2}}{k_{⊥}^{2}} \frac{4 ω^{2} v_{s}^{2}}{R^{2}} .

…”

Section: Mhd Approachmentioning

confidence: 99%

“…Theoretical investigation of the Alfvén waves in such regions is complicated by their coupling with the compressional modes. In the MHD treatment, the Alfvén wave is coupled with the slow mode [ Walker , ; Klimushkin , ; Mazur et al , ]. This problem can be avoided if it is taken into account that the Alfvén mode usually has much shorter period than the slow mode [ Cheng et al , ; Leonovich and Kozlov , ].…”

Section: Introductionmentioning

confidence: 99%

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The Alfvén mode gyrokinetic equation in finite‐pressure magnetospheric plasma

Klimushkin

Mager

2015

JGR Space Physics

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The paper is concerned with the derivation of the Alfvén mode equation in finite‐pressure space plasma in gyrokinetic approach. The long plasma approximation is used, where the bounce frequency is much lower than both wave and drift frequencies. The only ultralow frequency mode in the long plasma approximation is the Alfvén‐ballooning compressional mode, which is described by the Alfvénic dispersion relation with some additional (ballooning) terms caused by the field line curvature and plasma pressure effects. Due to these effects the Alfvén mode acquires also considerable parallel magnetic field component. The long plasma approximation allowed us to consider the correspondence between the gyrokinetic and MHD approaches for the Alfvén mode equation. It is shown that in 0 < β ≪ 1 case, MHD approach gives correct Alfvén wave description, where β is plasma to magnetic pressure ratio.

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“…The wave's two‐dimensional electric field

{\overset{E}{true}}_{⊥}

{\overset{E}{true}}_{⊥} = - \nabla_{⊥} ψ .

…”

Section: Mhd Approachmentioning

confidence: 99%

((), ω^{2} - k_{∥}^{2} v_{A}^{2} - \frac{k_{y}^{2}}{k_{⊥}^{2}} \frac{2 P^{'}}{ρR}) ((), ω^{2} - k_{∥}^{2} v_{s}^{2}) = \frac{k_{y}^{2}}{k_{⊥}^{2}} \frac{4 ω^{2} v_{s}^{2}}{R^{2}} .

…”

Section: Mhd Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Alfvén mode gyrokinetic equation in finite‐pressure magnetospheric plasma

Klimushkin

Mager

2015

JGR Space Physics

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“…At least qualitatively, all the studies demonstrated that the ballooning modes can most probably trigger substorm‐related plasma instabilities at a distance of near‐Earth magnetotail, where numerous measurements indicated phenomena associated with the onset of substorms [e.g., Kisabeth and Rostoker , ; Lopez and Lui , ; Sergeev et al , ; Frank and Sigwarth , ; Chen et al , ; Meng and Liou , ; Akasofu et al , ; Xing et al , ; Panov et al , ]. Especially, based on Voigt 's configuration model of the magnetotail at the self‐consistent equilibrium, on the one hand, Zhu et al [] found that k y is proportional to the growth rate, and, at a large k y , the growth reaches a saturated value; on the other hand, Mazur et al [] provided the instability threshold and stop bands of both the stable Alfvén‐type and stable/unstable slow magnetosonic‐type modes under arbitrary k y conditions.…”

Section: Introductionmentioning

confidence: 99%

“…The previous studies on the ballooning mode are important to shed light on substorm physics, particularly the triggering process of the impulsive magnetic events in the near‐Earth magnetosphere and auroral ionosphere, as well as the low‐frequency oscillations in the plasma sheet generated by some impulsive source at the center of the magnetotail, propagating toward both dawn and dusk. Nevertheless, as pointed out by Mazur et al [], the exact expressions of the dispersion equation derived by different pioneer authors happened to be somewhat different from each other [e.g., among those provided by Safargaleev and Maltsev , , Ohtani and Tamao , , and Liu , ]. More seriously, these theoretical analysis of the ballooning instability encountered difficulties to recover the basic shear Alfvén mode and the magnetosonic mode in uniform, ideal plasmas, namely [e.g., Boyd and Sanderson , ; Bellan , ],

ω^{2} = c_{A}^{2} k_{z}^{2}; ω^{4} - ((), c_{A}^{2} + γ c_{s}^{2}) k^{2} ω^{2} + γ c_{A}^{2} c_{s}^{2} k^{2} k_{z}^{2} = 0

and the fundamental ballooning mode in incompressible plasmas, namely [e.g., Kadomtsev , ; Mikhailovskii , ; Hirose et al , ; Hirose and Joiner , ],

ω^{2} = c_{A}^{2} ((), k_{z}^{2} - β k_{p} k_{c}) and γ_{BM}^{2} = 2 c_{s}^{2} k_{p} k_{c}

where in equations and , ω is the wave frequency, c A and c s are the Alfvén and sound speeds, respectively, k and k z are the total and the parallel wave numbers, respectively, γ and β are the adiabatic index and plasma beta number, respectively, k p and k c are the averaged inverse scale length of the pr...…”

Section: Introductionmentioning

confidence: 99%

Effect of heat flux on Alfvén ballooning modes in isotropic Hall‐MHD plasmas

2014

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The magnetosphere undergoes a transition from a dipole-like to taillike structure in the antisunward direction. In this region, Alfvén ballooning instability has been considered as a leading candidate to be responsible for the onset and expansion phase of observed impulsive substorms. We apply the generalized Ohm's law in isotropic Hall-MHD equations and study the effect of heat flux on the ballooning modes under substorm circumstances. The set of partial differential equations is obtained for a general ballooning dispersion relation from which all classical Alfvén waves and fundamental ballooning modes are recovered, e.g., the decoupled shear Alfvén and magnetosonic modes, the classical ballooning instability in incompressible plasmas. In the absence of the heat flux, the ballooning mode is featured by the coupling of the two modes by the superposition of the independent Hall effect and the independent plasma inhomogeneity effect. By contrast, heat flux exerts its influence on the ballooning mode by updating the coefficients of the terms in the dispersion relation. The results expose that the growth rate ( BM ) has two branches. If k p is free, one branch shifts versus , while the other branch is damped substantially by the heat flux, leading to a more stable ballooning mode; if k c is free, one branch shifts little versus , but the other one has higher BM driven by the heat flux, leading to a more unstable ballooning mode.

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Revisit of Alfvén ballooning modes in isotropic, ideal MHD plasmas: Effect of diamagnetic condition

John

Hirose

2014

JGR Space Physics

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Alfvén ballooning modes provide an important mechanism to explain explosive phenomena in regions where field lines transit from dipole-like to taillike shapes. However, commonly used analytical results were unable to recover Alfvén modes in uniform plasmas and basic ballooning mode in inhomogeneous plasmas. We rigidly revisited previous work on isotropic, ideal magnetospheric plasmas and found where the problems occurred. This paper shows accurate expressions of the ballooning modes. Under the dimagnetic condition (an infinite k y ), the modes have two groups depending on the relations of the three equilibrium parameters: plasma , pressure gradient k p , and magnetic curvature k c (magnetic gradient k B is no more than a tenth of k c and thus neglected in magnetotail plasma). If the constraint is relaxed (a finite k y ), the dispersion relation includes the following: (1) the fast compressional Alfvén branch; (2) two groups of ballooning instabilities: Group 1 appears when k p is independent of , and Group 2 emerges when k c is independent of ; and (3) in Group 1, a critical exists above which the wave mode becomes unstable, while the perpendicular wave number (k ⟂ ) affects the instability by modulating the critical values; by contrast, in Group 2, there is no critical , and the wave keeps its original stable or unstable mode, while k ⟂ has a critical value above which the wave mode becomes unstable.

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Ballooning modes and their stability in a near-Earth plasma

Cited by 21 publications

References 23 publications

The Alfvén mode gyrokinetic equation in finite‐pressure magnetospheric plasma

The Alfvén mode gyrokinetic equation in finite‐pressure magnetospheric plasma

Effect of heat flux on Alfvén ballooning modes in isotropic Hall‐MHD plasmas

Revisit of Alfvén ballooning modes in isotropic, ideal MHD plasmas: Effect of diamagnetic condition

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