3 rd Asia-Pacific Conference on Plasma Physics, Hefei, China Kinetic Eulerian Simulation of Electrostatic Phase Space Vortices (PSVs) In A Driven-Dissipative Vlasov-Poisson System Pallavi Trivedi †* , Rajaraman Ganesh * † P rincetonP lasmaP hysicsLaboratory, P rinceton, U SA * InstituteF orP lasmaResearch, HBN I, Gandhinagar, Gujarat, India November 6, 2019 [email protected]
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3rd Asia-Pacific Conference on Plasma Physics, Hefei, China
Kinetic Eulerian Simulation ofElectrostatic Phase Space Vortices
(PSVs) In A Driven-DissipativeVlasov-Poisson System
Pallavi Trivedi†∗,Rajaraman Ganesh∗
†PrincetonPlasmaPhysicsLaboratory, Princeton, USA
∗InstituteForP lasmaResearch,HBNI,Gandhinagar,Gujarat, India
Vlasov equation give accurate description of weakly correlatedcollisionless plasmas and have a wide range of applications:-
from interplanetary environment to laboratory plasmas
to understand kinetic effects of plasmas such as wave particleresonant interactions,
to understand damping effects, instabilities, nonlinear particletrapping, several nonlinear coherent structures, double layers inlaboratory plasmas and more.
Energetic particles produced in fusion experiments, solar wind andmagnetospheric plasmas etc can excite various modes and leads tovarious frequency bursts over the spatial and temporal scales.
Associated nonlinear wave-particle interactions can generatesignificantly enhanced levels of energetic particle transport which canhappen both along and across the magnetic field lines. [For example,increased energetic particle transport by Alfven eigenmodes has beencorrelated with a fast frequency oscillation (chirping) with asubmillisecond period that has been observed in many experiments].[Zhang et. al., PRL 109, 025001 (2012)]
Several investigations aim to understand the features of dynamics ofwave-particles interaction such as excitation of electrostatic modes andphase space structures, at ion scales and electron scales in spaceplasmas by analyzing both spacecraft data, solar wind observationsand numerical results from kinetic or phase spacesimulations.[Valentini et.al., Fajans et.al., Berk et.al.]
In systems governed by kinetic processes, limit of lowcollisionality is not the same as the limit of zero collisionality.
Particle collisions work to restore thermal equilibrium, which caneventually change the features of the kinetic dynamics of aplasma, even in situations where collisionality can be consideredvery weak.
In these conditions,
Kinetic processes works to produce deformations of the particledistribution function away from a Maxwellian
Collisionality tends to restore the Maxwellian configuration.
The evolution of the plasma is, therefore, a result of complexcombination of these two effects.
A simplest approach is to model the unbounded or periodicdirection (eg toroidal direction in Tokamaks or along the B-fieldin Astroplasmas) using a 1D-1V Vlasov-Poisson model where anexternal electric field is used to produce kinetic species.
In the limit of zero correlations and weak collisions, plasmas arewell described in their electrostatic limit by Vlasov-Poisson (VP)system of equations.
Vlasov Equation-1D
∂fj∂t
+−→vj .∂fj∂−→x
+qjmj
(−→E +−→v ×
−→B ).
∂fj∂−→vj
= 0
Along the B-field or in absence of B-field : −→v ×−→B = 0.
Also known as Lenard-Bernstein collisional operator.
Dissipative operator
Fokker-Planck form which preserves:-
conservation the number of electrons;represent diffusion in velocity space;
P.L. Bhatnagar; E.P. Gross; M. Krook, Physical Review. 94 (3) 511525,(1954).V. E. Zakharov and V. I. Karpman, Sov. Phys. JETP 16, 351 (1963).A. Lenard and I. B. Bernstein, Phys. Rev. 112, 1456 (1958).
A common characteristic of an evolving nonlinear system is thatthe mode frequency also evolves in time. Such behavior, referredto as frequency chirping/sweeping, is normally a relaxationprocess.
It can be found in nonlinear optics, developing turbulent systems,and unsaturated nonlinear wave-wave and/or wave-particleinteraction, in particular, beam driven activities in tokamakplasmas.
Previously, a homogeneous plasma with Maxwellian velocitydistribution is driven with an external drive of time dependentfrequency ω(t) for time interval ∆td → PSVs.
Pallavi Trivedi and R. Ganesh, Phys. of Plasmas 23, 062112 (2016)
Pallavi Trivedi and R. Ganesh, Phys. of Plasmas 24, 032107 (2017)
Pallavi Trivedi and R. Ganesh, Manuscript in communication (2019)
Electrostatic PSVs : On applying a small (linear-like) amplitude,external drive, when chirped downwards, it is shown to coupleeffectively to the plasma and increase both streaming of“untrapped” and “trapped” particle fraction.
To understand dissipative effect of weak collisions on drivenPSVs, two operators have been applied:-
Using both collisional operators, it is shown that for weakcollisions (eg. 10−5), the giant PSVs smoothen out, yet retainlarge excess density fractions.