What is Role of Proton Beams in Solar Radio Bursts? Jun-ichi Sakai Laboratory for Plasma Astrophysics University of Toyama, Japan

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What is Role of Proton Beams in Solar Radio
Bursts? Jun-ichi Sakai Laboratory for Plasma
Astrophysics University of Toyama, Japan
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Motivation

• It is believed that solar radio bursts like Type
  III and Type II are generated from electrons
  accelerated in the solar flare region or from
  electrons accelerated near the fast magnetosonic
  shock front.
• It is recognized that some protons can be
  accelerated by surfing mechanism near the fast
  magnetosonic shock front. And also some protons
  are reflected and accelerated near the shock
  front, resulting in proton beams.

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Contents

• Proton acceleration by shocks--Surfing
  acceleration
• Examples of shock formation
• Wave emission from proton beams
• Conclusions

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Simulation Model
Magnetic Field Line
Shock Wave
Model(2)qlt90
CME
q
90
v
Model(1)90
v
Solar surface
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Simulation Model

• Two-dimensional fully relativistic
  electromagnetic Particle-In-Cell code.
• System size Lx800, Ly10
• The free boundary condition in the x-direction,
  and the periodic boundary condition in the
  y-direction are imposed.

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Initial Conditions and Parameters
Model(1)
10
y
v
B0
0
Model(2)
10
x
0
200
800
Mass ratio mi64me Plasma beta ?0.05
(?ce/?pe0.632) ?ceElectron cyclotron
frequency ?peElectron plasma frequency Alfvén
velocity vA0.08c (clight
velocity)
B0 n4n0400 v3vA0.24c
BB0 nn0100 v0
EvB (EzvyBx)
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Parameter Runs

• Alfvén Mach (v/vA) 3, 2, 1.5
• Propagation Angle (q) 90, 80, 70
• (for
  Mach3)
• 90,
  70, 40
• (for
  Mach2 and 1.5)
• Our simulation results are based on Alfvén Mach
  is 3 and Propagation Angle is 80.

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Wave Emission Process
Shock region
Ex
Ex
x
(?pet0)
1.Some electrons are reflected behind the
shock front. 2.The reflected electrons behind
the shock front mix up with the in-coming
electrons due to the counter- streaming
instability. 3.Then there appear the electro-
static waves behind the shock.
vix/c
vex/c
x
(?pet90)
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Particle Acceleration
Shock region
By
By
x
(?pet0)
viz/c
Both electrons and ions are strongly accelerated
in the z- direction near the shock front through
the surfing mechanism.
vez/c
x
(?pet90)
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Surfing Acceleration byElectrostatic wave
propagating perpendicular to magnetic field
Equation of Motion
ExE0sin(?t-kx) ByB0
Solve for vz In moving frame
y
Ex
e
Acceleration Factor
x
z
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Spatial Distribution of Ex and Ez
(?pet66)
(?pet18)
Ex
Ez
x
x
Red arrow area (x70?326) are used to find the
dispersion relation of Ex. Blue arrow area
(x540?796) are used to find the dispersion
relation of Ez.
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Dispersion Relations of Ex and Ez
Elecrostatic Langmuir Waves (Z-mode) are
generated in the yellow contour line.
?/?pe
?/?pe
EM Waves are excited.
kc/?pe
kc/?pe
Ex
Ez
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Conclusions

• We found the wave emission process of Solar Type
  II Radio Bursts associated with CME.
• We also found that fast magnetic shock wave is
  formed with both protons and electrons
  accelerated by the surfing mechanism.

1. Some electrons are reflected behind the
shock front. 2. Reflected electrons generate
electrostatic waves. 3. They could be
converted to the extra-ordinary
electromagnetic waves through the Direct
Linear Mode Conversion.
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1.Generation of magnetosonic shocks during
collision of two current loops

• PIC simulation
• Force-Free magnetic configuration
• JB 0
• Uniform density and uniform temperatur
• System size
• 900 900
• n0100
• Loop position (300, 300) (600, 600)
• Loop radius 100

Simulation System
y
x
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2.Generation of magnetosonic shock during
formation of current sheet
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Emission of electromagnetic waves by proton beams

• The proton beams propagating to the low-density
  region are forced to move, together with the
  background electrons, to keep charge neutrality,
  resulting in the excitation of electrostatic
  waves
• proton beam modes and Langmuir waves.
• In the early stage of electrostatic wave
  excitation, both R and L modes near the
  fundamental plasma
• frequency can be generated along a uniform
  magnetic field.
• It is also found that, in the late stage, the
  second harmonics
• of electromagnetic waves can be excited through
  the interaction of three waves. During these
  emission processes, proton
• beams can move along the magnetic field almost
  without losing their kinetic energy.

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Electron(solid line) and Proton(dashed line)
velocity distribution(a) t0 and (b) ?pet1500
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• Sakai and Nagasugi (2007) investigated the
  dynamics of proton beams propagating along a
  uniform magnetic field, as well as across the
  magnetic field in nonuniform solar plasmas,
  paying attention to the emission process of
  electromagnetic waves to understand a new
  solar-burst component emitting only in the
  terahertz range during the solar flare observed
  by Kaufmann et al.(2004).

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Proton beams propagating into high density region
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• From the simulation where the proton beams
  propagate along a uniform magnetic field into the
  high-density region, it is found that strong
  electromagnetic waves are generated behind the
  proton beams. When the proton beams propagate
  perpendicular to the magnetic field, the
  extra-ordinary mode can be excited from two
  electron Bernstein waves through three-wave
  interactions. These simulation results could be
  applied to the electromagnetic wave emission from
  the solar photosphere during the solar flares.

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Conclusions

• 1.Protons can be accelerated by surfing mechanism
  in shock front
• 2.Proton beams play an important role for the
  emission of electromagnetic waves

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• The role of proton beams reflected in the fast
  magnetosonic shock front is also discussed for
  the emission mechanism of the Type II radio
  bursts.

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Shock formation and double structure(60 degree)
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Time History of Ex and Ez
Ex
Ez
(Electrostatic)
(Electromagnetic)
Fundamental
Second harmonic
wpet
wpet
Parameters Red line w/wpe1.3 ?1.6,
kc/wpe0?2.5 Black line w/wpe1.5 ?2.0,
kc/wpe0?3.0 Blue line w/wpe2.5 ?3.5,
kc/wpe0?4.0
They are obtained by Inverse Fourier
Transformation using the data of dispersion
relations.