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ISSN No:-2456-2165
A Review on Mechanisms of
Turbulence Generation in Solar Corona
Prachi Sharma1* and R. P. Sharma2
1
Department of Applied Science, Madhav Institute of Technology & Science, Gwalior-474005, India
2
Centre for Energy Studies, Indian Institute of Technology Delhi-110016, India
Abstract:- The unusual heating of solar corona is Observations of Hinode spacecraft have also predicted the
always a fascinating question in front of astrophysics role of Alfvén waves in the heating of coronal plasma [3].
community. In fact, this high temperature (T > 106 K) of MHD waves and ion acoustic waves are generated in the
solar corona is directly associated with the generation of photosphere and the waves which are produced in the
solar wind. photosphere must be dissipated in the outer atmosphere to
increase its temperature. Therefore, ion acoustic waves
There are models like Landau damping of plasma have also been considered of great interest to heat the solar
waves, anisotropic turbulence and many more available coronal region [4]. Rial et al., 2010 [5], examined the
to explain both the phenomena, the unexpected heating temporal evolution of coupled three-dimensional
of the corona and solar wind acceleration. Existence of propagating fast and Alfvén waves in a potential coronal
waves in and around this region is believed to be arcade. They concluded that due to the involvement of
reasonable cause for this extraordinary heating. three-dimensional dependency on the perturbed quantities,
Turbulence generation as a result of nonlinear as a result, coupling of fast and Alfvén waves takes place
interaction between these waves found to be most and the obtained solutions demonstrate a mixed fast/Alfvén
significant phenomena for this abnormal heating. The characteristics. The investigated medium is non-uniform
present article accommodates some paramount and coupling of resonant nature produces so that energy
conclusions that shows the impression of turbulence to transfer and damping of wave exhibit in the considered
assist the heating of particles in solar coronal regime. medium.
Where
E k
represents the energy per unit mass and
III. GENERATION OF KOLMOGOROV
TURBULENCE BY WAVE’S INTERACTION
Ꜫ shows the energy dissipation rate per unit mass.
v2 E k dk
0
The interplay of inertial Alfvѐn wave with slow
magnetosonic wave has been studied by Sharma et al.,
2016a [9] in solar corona. These waves were propagating in
32
all the three directions. This interaction gives rise to the
2 v2 filamentation like instability. The analysis of field intensity
k
0 3c
of inertial Alfvén wave shows the localized structures with
0 the pre-existing slow magnetosonic waves in the
(2) background. The pattern of energy transferring to the small
scale modes is also predicted with this model. An attempt
v2 has been made to calculate the thermal tail of charged
is the non-thermal velocities in coronal loops and particles in solar coronal space with the help of second
k
0 is wave number at which energy injection starts. It scaling in the spectrum of magnetic power which was
2 found after the first break point. Thus due to the nonlinear
is something like diameter of the active region coupling between these two waves, filamentation and
loops. The typical values are- formation of thermal tail takes place. In this model, the
interaction between coronal particles and the localized
fields studied with fractional diffusion approach. How the
v2 1.81013 cm2 s2 power law tail generated because of turbulence related to
, the fractional diffusion mechanism has been understood by
k 2.1109 cm1 Bian and Browning, 2008 [10].
0 .
In this diffusion mechanism, at the given time, the
Volumetric heating rate comes out to be- relation between the distribution function g v,t with
8 104 ergs cm3 s1 1
0 where loop density the spectral index is given by g v ~ v
. The
5 1015 gmcm3
0 . power spectrum studied by Sharma et al., 2016a [9] shows
that spectral index is having the numerical value 3
If the heating extends over the entire loop length then
energy flux density is (see Fig. 1), therefore the resultant distribution function can
U 8106 e rgs cm2 s1 8000 W m
2 be represented as g v ~ v4 . Hence there would be the
.
enhancement of the thermal tail of the charged particles,
which might be play an important role to accelerate the
particles.
2
Fig 1:- The plot of Ak and the perpendicular wave numbers taking the average over all parallel wave numbers [9].
Fokker–Planck diffusive mechanism is one of the Sharma et al., 2016b [13] discussed the coupling of
mechanisms which can explain the particle acceleration. three dimensionally propagating kinetic Alfvén wave and
Sharma and Kumar, 2010 [11] has made an attempt to ion acoustic wave which is also propagating in all three
study the Fokker–Planck diffusive formalism in auroral dimensions in solar coronal loops. Field structures of
plasmas. They described the interaction in a continual kinetic Alfvén wave gets localized in the influence of its
manner between auroral particles and localized structures changed phase velocity as a result of variations in
of intense fields using the diffusion theory with a quasi- background density. From the obtained results from
f f
numerical simulation, the size of the localized structures on
linear approach, represented as D v ; transverse scale is found to be of the order of gyro radii
t v v scales. Laser beam filamentation is quite analogous to this
localization process in the presence of nonlinearity, where
here D(v) represent the diffusion coefficient and f (t,v) is there is a race between the nonlinear effects and diffraction.
the distribution function in velocity space. Since the When the beam’s transverse size is higher than critical
characteristic time is neglected in comparison to value, the nonlinear effects command the diffraction effects
observation time and hence distribution function becomes and as a result, localization of the beam takes place. Energy
independent of time and represented as f (v) ∝ v2−η. spectrum has also been tried to study with one restriction
i.e., by taking the average over all parallel wavenumbers
Numerous predictions have been put forward by the (when the spectrum shows quasi steady state of turbulence)
researchers to investigate the mechanisms of particle as an outcome of coupling of these two waves with the
acceleration. Fisk and Gloeckler, 2008 [12] have been presence of ponderomotive nonlinear force. Energy cascade
found the compressional turbulence causes the particle 5/3
acceleration in a thermally isolated environment with the has been obtained with the scale of k (known as
spectral shape f (v) ∝ v−5of the thermal tail. Acceleration Kolmogorov scaling) up to k s 1 as shown in fig. 2.
with a high speed of the charged particles has also been
discussed as a result of evolution of power spectrum with
the advancement of time.
2
Fig 2:- The plot of Ak and the perpendicular wave numbers taking the average over all parallel wave numbers [13].
The interaction between the high frequency (~0.01 changes due to this ponderomotive force. This interplay
Hz) and low frequency (~0.001 Hz) slow magnetosonic between high and low frequencies waves gives rise to the
waves have been examined in the solar coronal loops by focusing type results of high frequency wave and field
Sharma et al., 2017 [14]. They adopted two-fluid model to localized structures appeared. Variation analysis of energy
study this self modulation of slow magnetosonic waves, verses wavenumber has also been checked. The reason
simulate the normalized equations of both the waves with behind to study this spectrum is exactly to know the idea
numerical technique of pseudo-spectral method. This about scaling around the inertial range. As expected, the
attempt was made to predict the reason behind the scale of energy cascading is just the Kolmogorov type (-
Kolmogorov turbulence via self modulation of 5/3) in the inertial range of the power spectrum (see Fig. 3).
experimentally observed slow magnetosonic waves in the The compatibility of Kolmogorov dissipation rate with
region of coronal loop. These waves interact with each heating requirements has already been discussed above,
other via ponderomotive nonlinear force which is arises due hence this wave based model is quite reliable for generating
to high frequency of pump wave. The low frequency wave the turbulence in coronal loops.
is travelling in the ambient magnetic field and its dynamics
2
Fig 3:- The plot of Bk versus k x with average of all k z [14].
REFERENCES