You are on page 1of 5

Volume 5, Issue 4, April – 2020 International Journal of Innovative Science and Research Technology

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.

Keywords:- Plasma Waves, Turbulence, Solar Corona. II. HEATING BY MAGNETOHYDRODYNAMIC


TURBULENCE
I. WAVES IN CORONA
Solar coronal heating problem can be analyzed by
The presence of different modes of waves have giving the attention only on two major points that is what is
always involved to get the possible solution for the many the source of that energy which is available for anomalous
unsolved mysteries around space. The possible cause for heating of corona and from where it comes i.e., the reason
waves to become an important reason for coronal heating is behind the mechanism to produce sufficient energy which
that magnetohydrodynamic (MHD) waves are the mediator will assist the heating of the particles. In this article, the
of energy transfer from convective zone beneath the Sun’s discussion is around possible mechanisms only as
photosphere up to the solar atmosphere at the time of compared to the source. Turbulence is always fascinating
travelling into the magnetized plasmas. There, the Alfvén factor to affect the coronal heating. It plays an important
waves could turn into shock waves that dissipate their role to create cascading of energy to heat the particles in
energy as heat that will cause to increase the temperature of and around corona.
the corona. Different waves that deliver heat to the coronal
particles sounds impressive but there should be some Coronal heating is believed to be affected by
results for the sake of accuracy with this wave based magnetohydrodynamic turbulence [6]. Interaction of kinetic
model. Alfvén wave with electrons has been considered an
important acceleration mechanism and participated in the
SOHO (solar and heliospheric observatory) and coronal heating problem affectively [7]. Footpoint motions
TRACE (Transition Region and Coronal Explorer) are accepted as a most possible cause in the photosphere to
missions have been predicted the presence of different type provide energy into the large scale modes. Now the
of oscillations which is having small amplitude in the magnetohydrodynamic turbulence transfers this energy to
coronal loop region. Slow MHD waves have been the modes of small scales. Active regions, quiet-sun regions
experimentally observed by the data of these spacecrafts and coronal holes are three different classification of solar
and the resolution of these spacecrafts are very high in both corona. Active regions are just the ensembles of loop like
space and time domain. The low-frequency modes of structures in the photosphere which connects the points of
magnetized plasmas, Alfvén waves, were theorized by opposite magnetic polarity. Hollweg, 1984 [8] predicted
Alfvén, 1947 [1] and dissipates in corona. Due to their that Kolmogorov turbulent dissipate rate is good enough to
dissipation, Alfvén wave considers effective candidate in meet the heating requirements for coronal active region
the puzzle of coronal heating. Observations confirm the loops. The Kolmogorov flux is found to be lying in the
presence of Alfvén waves in the solar corona [2].

IJISRT20APR786 www.ijisrt.com 932


Volume 5, Issue 4, April – 2020 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
range of requirement to heat the active region. He Thus on the behalf of above analysis, Hollweg [8]
calculated in the following manner: predicted that the Kolmogorov turbulent dissipation rate is
enough for the heating of particles in the coronal active
The dissipation rate in turbulent cascade depends only region but the mechanisms for the generation of this
on how rapidly the energy is cascaded. turbulence in coronal region were the unsolved mysteries
2 5 for the scientists around the world. To investigate the
E k
 
 c  3k
0 
3  possible mechanisms for Kolmogorov turbulence in solar
corona, many researchers considered waves as a key factor
(1) and studied the interaction between them.

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 1.81013 cm2 s2 power law tail generated because of turbulence related to
, the fractional diffusion mechanism has been understood by
k  2.1109 cm1 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 104 ergs cm3 s1 1 
  
0 where loop density the spectral index is given by g  v  ~ v  
. The
  5 1015 gmcm3
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  8106 e rgs cm2 s1  8000 W m
2 be represented as g  v  ~ v4 . 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.

IJISRT20APR786 www.ijisrt.com 933


Volume 5, Issue 4, April – 2020 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165

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.

IJISRT20APR786 www.ijisrt.com 934


Volume 5, Issue 4, April – 2020 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165

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].

IJISRT20APR786 www.ijisrt.com 935


Volume 5, Issue 4, April – 2020 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
IV. FINAL REMARKS [11]. Sharma, R. P., Kumar, S.: Landau damped kinetic
Alfvén waves and coronal heating. J. Plasma Phys. 76,
How MHD turbulence is helpful in the process of 239 (2010).
coronal heating, it is clearly explained by Hollweg, 1984 [12]. Fisk, L.A., Gloeckler, G.: Acceleration of
[8]. The main objective of this article to discuss the various suprathermal tails in the solar wind. Astrophys. J. 686,
mechanisms to generate turbulence in the region of solar 1466 (2008).
corona. Waves that are observed in and around corona can [13]. Sharma, P., Yadav, N., Sharma, R. P.: Nonlinear
interact with each other via some nonlinearity and give rise interaction of kinetic Alfvén waves and ion acoustic
to energy cascading at the same scale which is compatible waves in coronal loops. Phys. Plasmas 23, 052304
with the required dissipation rate for heating. NASA’s (2016b).
Parker Solar Probe is the first ever breakthrough mission to [14]. Sharma, R. P., Sharma, P., Yadav, N.: Self
touch the sun. Cranmer, 2018 [15] showed some theoretical Modulation of Slow Magnetosonic Waves and
predictions about MHD turbulence in the regions to be Turbulence Generation in Solar Coronal Loops. Phys.
explored by PSP. He studied 3-D power spectra with Plasmas 24, 012905 (2017).
perpendicular wavenumber of incompressible Alfvén [15]. Cranmer, S.R.: Some turbulent predictions for Parker
waves and fast-mode waves as a function of radial distance solar probe. arXiv preprint arXiv:1808.09477 (2018).
from the sun and confirmed the importance of kinetic
Alfvén wave in energy cascading. Therefore waves
interaction can be consider most effective way for
generating turbulence in coronal plasma that will gradually
increase the transportation of energy and ultimately heat the
particles.

REFERENCES

[1]. Alfvén, H.: Granulation, magneto-hydrodynamic


waves, and the heating of the solar corona. Mon. Not.
Roy. Astron. Soc. 107, 211 (1947).
[2]. Tomczyk, S., McIntosh, S. W., Keil, S. L., Judge, P.
G., Schad, T., Seeley, D. H., Edmondson, J.: Alfvén
waves in solar corona. Science 317, 1192 (2007).
[3]. De Pontieu, B., McIntosh, S. W., Carlsson, M.,
Hansteen, V. H., Tarbell, T. D., Schrijver, C. J., Title,
A. M., Shine, R. A., Tsuneta, S., Katsukawa, Y.,
Ichimoto, K., Suematsu, Y., Shimizu, T., Nagata, S.:
Chromospheric Alfvénic waves strong enough to
power the solar wind. Science 318, 1574 (2007).
[4]. D'Angelo, N.: Heating of the solar corona. Sol. Phys.
7, 321-328 (1969).
[5]. Rial, S., Arregui, I., Terradas, J., Oliver, R., Ballester,
J. L.: Three dimensional propagation of
magnetohydrodynamic waves in solar coronal
arcades. Astrophys. J. 713, 651 (2010).
[6]. Zank, G. P., Adhikari, L., Hunana, P., Tiwari, S. K.,
Moore, R., Shiota, D., Bruno, R., Telloni, D.: Theory
and transport of nearly incompressible
magnetohydrodynamic turbulence. IV. Solar coronal
turbulence. Astrophys. J. 854, 32 (2018).
[7]. Malara, F., Nigro, G., Valentini, F., Sorriso-Valvo, L.:
Electron heating by kinetic Alfvén waves in coronal
loop turbulence. Astrophys. J. 871, 66 (2019).
[8]. Hollweg, J. V.: Resonances of coronal loops.
Astrophys. J. 277, 392 (1984).
[9]. Sharma, P., Yadav, N., Sharma, R. P.: Nonlinear
evolution of 3-D Inertial Alfvén Wave and its
implication in particle Acceleration. Sol. Phys. 291,
931 (2016a).
[10]. Bian, N.H., Browning, P. K.: Particle acceleration in a
model of a turbulent reconnecting plasma: A
fractional diffusion approach. Astrophys. J. Lett. 687,
L111 (2008).

IJISRT20APR786 www.ijisrt.com 936

You might also like