Influence of the transport regime on the energetic particle density profiles upstream and downstream of interplanetary shocks

Prete, Giuseppe; Perri, S.; Zimbardo, G.

doi:10.1016/j.asr.2019.01.002

Cited by 8 publications

(10 citation statements)

References 46 publications

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“…Compared to the case of normal diffusion, which would give an exponential profile, we can see that in the case of superdiffusion and advection the density profile obtained by considering only the left contribution to the flux is steeper close to the source of particles at x = 0, and more shallow than an exponential farther away. This is similar to the behavior found for energetic particles propagating upstream of interplanetary shock waves [12,13,45,51,55] and upstream of supernova remnant shocks [56,57].…”

Section: Solutions With the Left Contribution Onlysupporting

confidence: 83%

“…We recall that several definitions of fractional derivatives are available [36,40,50], and that this variety reflects the enhanced possibility offered by fractional derivatives to adapt the non-local flux operator, corresponding to the fractional Fick's law, to the diverse physical systems under consideration. In particular, in space plasmas the density of high-energy particles upstream of a shock wave is found to exhibit a sharp decrease close to the shock, and a slow power-law decay far upstream [12,13,33,43,47,51]. Such energetic particle density profiles are very similar to the properties of the Mittag-Leffler functions shown above.…”

Section: Discussionsupporting

confidence: 63%

“…The solution of the above fractional diffusion equation gives information on the time evolution of the particle density n(x, t); for instance, if the initial distribution is a delta function, at later times the density becomes a Lévy distribution of time-increasing width, shifted towards the direction of the flow [5,37,39,51]. Less attention has been given to steady-state solutions of the transport problem, corresponding to studying the flux-gradient relationship which is expressed by the fractional Fick's law.…”

Section: Steady-state Solutions Of Fractional Diffusion-advection Equmentioning

confidence: 99%

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On the Fractional Diffusion-Advection Equation for Fluids and Plasmas

Zimbardo

Perri

2019

Fluids

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The problem of studying anomalous superdiffusive transport by means of fractional transport equations is considered. We concentrate on the case when an advection flow is present (since this corresponds to many actual plasma configurations), as well as on the case when a boundary is also present. We propose that the presence of a boundary can be taken into account by adopting the Caputo fractional derivatives for the side of the boundary (here, the left side), while the Riemann-Liouville derivative is used for the unbounded side (here, the right side). These derivatives are used to write the fractional diffusion–advection equation. We look for solutions in the steady-state case, as such solutions are of practical interest for comparison with observations both in laboratory and astrophysical plasmas. It is shown that the solutions in the completely asymmetric cases have the form of Mittag-Leffler functions in the case of the left fractional contribution, and the form of an exponential decay in the case of the right fractional contribution. Possible applications to space plasmas are discussed.

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Section: Solutions With the Left Contribution Onlysupporting

confidence: 83%

Section: Discussionsupporting

confidence: 63%

Section: Steady-state Solutions Of Fractional Diffusion-advection Equmentioning

confidence: 99%

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On the Fractional Diffusion-Advection Equation for Fluids and Plasmas

Zimbardo

Perri

2019

Fluids

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“…Профили функции распределения ионов водорода с различной энергией в момент времени t = 1800 −1 от начала моделирования показаны на рис. 1, a. Качественно их вид хорошо вопроизводит наблюдаемые профили функции распределения в солнечном ветре (см., например, работу [16]). На нижних панелях приведены профили скорости потока и турбулентной составляющей магнитного поля, использовавшиеся в интеграле (9) и выражении (1).…”

Section: диффузия ускоренных протоновunclassified

Моделирование Диффузии Ускоренных Частиц В Бесстолкновительных Ударных Волнах С Примесью Ионов Тяжелее Водорода

Кропотина¹,

Быков²,

Осипов³

et al. 2020

Журнал Технической Физики

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Представлены результаты гибридного моделирования диффузионного ускорения ионов с различным соотношением заряда к массе в квазипродольных бесстолкновительных ударных волнах. Рассмотрена водородная среда с динамически незначимой примесью ионов гелия и углерода в различных зарядовых состояниях. Определены пространственные области применимости бомовского приближения, а также квазилинейной теории диффузии. Обсуждается возможность недиффузионного распространения в областях далеко перед фронтом ударной волны. Ключевые слова: диффузия, бесстолкновительные ударные волны, космические лучи, квазилинейная теория.

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“…In the case of superdiffusion, the scattering times t i have a power-law-tailed probability distribution. The Monte Carlo model employed to generate the trajectories used for testing the anomalous diffusion diagnostics has extensively been used to bridge observations and models of anomalous transport in plasmas both for collisionless shocks and plasma turbulence (Prete et al 2019). In this model, it is possible to set the exponent µ of the power-law distribution of scattering times.…”

Section: Appendix A: Testing Tamsd With Monte Carlo Modelsmentioning

confidence: 99%

Particle transport in hybrid PIC shock simulations: A comparison of diagnostics

Trotta

Burgess

Prete

et al. 2019

Monthly Notices of the Royal Astronomical Society

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Recent in-situ and remote observations suggest that the transport regime associated with shock accelerated particles may be anomalous i.e., the Mean Square Displacement (MSD) of such particles scales non-linearly with time. We use self-consistent, hybrid PIC plasma simulations to simulate a quasi-parallel shock with parameters compatible with heliospheric shocks, and gain insights about the particle transport in such a system. For suprathermal particles interacting with the shock we compute the MSD separately in the upstream and downstream regions. Tracking suprathermal particles for sufficiently long times up and/or downstream of the shock poses problems in particle plasma simulations, such as statistically poor particle ensembles and trajectory fragments of variable length in time. Therefore, we introduce the use of time-averaged mean square displacement (TAMSD), which is based on single particle trajectories, as an additional technique to address the transport regime for the upstream and downstream regions. MSD and TAMSD are in agreement for the upstream energetic particle population, and both give a strong indication of superdiffusive transport, consistent with interplanetary shock observations. MSD and TAMSD are also in reasonable agreement downstream, where indications of anomalous transport are also found. TAMSD shows evidence of heterogeneity in the diffusion properties of the downstream particle population, ranging from subdiffusive behaviour of particles trapped in the strong magnetic field fluctuations generated at the shock, to superdiffusive behaviour of particles transmitted and moving away from the shock.

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Influence of the transport regime on the energetic particle density profiles upstream and downstream of interplanetary shocks

Cited by 8 publications

References 46 publications

On the Fractional Diffusion-Advection Equation for Fluids and Plasmas

On the Fractional Diffusion-Advection Equation for Fluids and Plasmas

Моделирование Диффузии Ускоренных Частиц В Бесстолкновительных Ударных Волнах С Примесью Ионов Тяжелее Водорода

Particle transport in hybrid PIC shock simulations: A comparison of diagnostics

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