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SUMMARY:Magnetic Island coalescence using Reduced Hall MHD Model
DTSTART;VALUE=DATE-TIME:20210514T162500Z
DTEND;VALUE=DATE-TIME:20210514T164500Z
DTSTAMP;VALUE=DATE-TIME:20211027T105843Z
UID:indico-contribution-17697@conferences.iaea.org
DESCRIPTION:Speakers: Jagannath Mahapatra (Institute for Plasma Research)\
nSearch for physical models which support increased magnetic reconnection
rates has proven to be an important pursuit in both laboratory plasmas suc
h as magnetic fusion plasma devices as well as in astrophysical plasmas. O
ver the years\, it has been realized that apart from ion Hall effect\, mag
netic field structure and flow field structure near a reconnection zone co
uld be crucial in realizing improved reconnection rates. In this work\, a
new reduced Hall magnetohydrodynamic model (RHMHD) [7] is used\, which cap
tures\, apart from the standard reconnection physics\, the Hall effect and
the effect of plasma flow field\, in the out-of-plane and in-plane direct
ions to the reconnection zone. Using magnetic island coalescence as a test
problem\, we report enhanced reconnection rates.\n\nSweet-Parker (SP) mod
el is one of the most studied analytical models to explain magnetic reconn
ection using resistive MHD equations\, according to which\, the rate of ma
gnetic reconnection $\\propto \\eta^{1/2}$ ($\\eta$ is the electrical resi
stivity). Hence\, for weakly resistive/collisional or collisionless system
s\, reconnection rate is slow compared to the observed high reconnection r
ate\, within this model. Besides resistive MHD model\, studies have been p
erformed using other physics models such as two-fluid Hall MHD model [5]\,
hybrid models [8]\, fully kinetic models [9]\, etc\, to understand variou
s aspects of magnetic reconnection. These studies have revealed the depend
ence of reconnection rate on various parameters such as Lundquist number (
$\\propto \\eta^{-1}$)\, system size\, guide field\, effect of electron in
ertia\, and more. Presence of a strong external magnetic field helps to st
udy magnetic reconnection using a more simpler model such as Reduced-MHD (
RMHD) model [1]. For low resistivity plasmas\, kinetic effects such as Hal
l effect is necessary to incorporate in one-fluid RMHD model. For example\
, two-potential incompressible Hall MHD model has been used to study self-
driven and externally driven magnetic reconnection [11]. Similarly\, a mor
e general model is Reduced Hall MHD (RHMHD) model [7]. RHMHD model is desc
ribed by solenoidal velocity and magnetic field\, generated from four scal
ar potentials. This RHMHD model has been tested in studying effect of Hall
physics in turbulence [7]\, but not much work has been done in the study
of magnetic reconnection.\n\nIn 2.5-Dimension\, when the Hall parameter (r
atio of ion skin depth to the characteristic length of the system) and per
pendicular potential components initialize to zero\, the RHMHD model reduc
es to Reduced MHD model [1]. In 3D\, even for extremely small values of Ha
ll parameter and zero perpendicular potential components\, this model reta
ins the helical nature of magnetic and velocity fields. These helical magn
etic and velocity components make the 3D flux tubes more realistic as foun
d in tokamak and solar corona. Hence\, this RHMHD model is perhaps more su
itable to investigate reconnection physics.\n\nOne of the important issues
is to investigate the role of Hall physics including the flow dynamics al
ong and across the guided $B$-field as flow critically controls the plasma
dynamics around reconnection zone. As a test case\, magnetic island coale
scence problem [3\,4\,6] has been studied to understand the physics of mag
netic reconnection. So\, in this work\, we investigate the island coalesce
nce problem using the ``Reduced Hall MHD (RHMHD)" model [7] in the incompr
essible limit using a vorticity-vector potential model within a single flu
id framework. As is well known\, using Fadeev's equilibrium [2]\, in the c
urrent island coalescence instability\, magnetic reconnection is driven by
the attraction force between two nearby parallel currents islands. The cu
rrent sheet thus formed between the islands\, because of this attraction f
orce\, acts as a reconnection site. In resistive MHD model\, for smaller r
esistivity values\, the flux pile-up in currents sheet inhibits further at
traction between the current isl7] is used\, which captures\, apart of the
standard reconnection physics\, the Hall effect and the effect of the pla
sma flow field\, in the out-of-plane and in-plane directions to the reconn
ection zone. Using magnetic island coalescence as a test problem\, we repo
rt enhanced reconnection rates.\n\nTo investigate some of these issues\, a
2D/3D Reduced MHD solver has been developed. Using this solver\, we addre
ss the evolution of Fadeev's equilibrium [2] when perturbed. We numericall
y calculate the eigenfunctions (SEE Fig.1 and Fig.2) and have compared our
results with those given in Ref. [4]. In Figure.3\, growth rate of island
coalescence instability for different island sizes has been plotted (from
our code and from Ref.4). To further benchmark our code in the limit of z
ero Hall parameter\, we have plotted time variation of the position of O-p
oint (see Fig.5) and compared our results with those of Ref.[5].\n![Eigenf
unctions of x-component of velocity from our code][a]\n![Eigenfunctions of
perturbed vector potential from our code][b]\n\n![Growth rate variation w
ith island size for Fadeev's equilibrium (Ref.[4])][c]\n![O-point position
of islands with resistivity (Ref.[5])][d]\n\nWith this model and a well-t
ested code\, we study current island systems for various values of above-s
tated parameters such as finite resistivity\, finite non-zero Hall paramet
er\, different magnetic island sizes\, etc. The effect of perpendicular c
omponent of vector potential and stream function in RHMHD model [7] is fou
nd to change the dynamics of island evolution. This\, in turn\, controls t
he evolution as well as reconnection rate of flux tubes in 3D. A detailed
study of these 2.5D island structures and 3D flux tubes will be presented.
\n\nReferences:\n[1] H. R. Strauss\, Phys. Fluids 19\, 134(1976).\n[2] V.
M. Fadeev et al.\, Nucl. Fusion 5\, 202(1965).\n[3] D. A. Knoll\, L. Chaco
n\, Phys. Plasmas 13\, 032307 (2006).\n[4] P. L. Pritchett et. al.\, Phys.
Fluids 22\, 2140 (1979).\n[5] D. A. Knoll\, L. Chacon\, Phys. Rev. Lett 9
6\, 135001 (2006).\n[6] D. Biskamp\, Phys. Rev. Lett 44\, 1069 (1980).\n[7
] D. O. Gomez et. al.\, Phys. Plasmas 15\, 102303 (2008).\n[8] K. D. Makw
ana et. al.\, Phys. Plasmas 25\, 082904 (2018).\n[9] W. Daughton et. al.\,
Phys. Rev. Lett. 103\, 065004 (2009).\n[10] A. Stainer et. al.\, Phys. Pl
asmas 24\, 022124 (2017).\n[11] L. F. Morales et. al.\, J. Geophy. Res. 11
0\, A04204 (2005).\n\n\n [a]: http://www.ipr.res.in/fec2020/images/Fig1_F
EC2020_JM.png\n [b]: http://www.ipr.res.in/fec2020/images/Fig2_FEC2020_JM
.png\n [c]: http://www.ipr.res.in/fec2020/images/Fig3_FEC2020_JM.png\n [
d]: http://www.ipr.res.in/fec2020/images/Fig4_FEC2020_JM.png\n\nhttps://co
nferences.iaea.org/event/214/contributions/17697/
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URL:https://conferences.iaea.org/event/214/contributions/17697/
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