motivation

What is Role of Proton Beams in Solar Radio

Bursts?

Jun-ichi Sakai Laboratory for Plasma Astrophysics

University of Toyama, Japan

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.

Contents

• Proton acceleration by shocks--Surfing acceleration

• Examples of shock formation

• Wave emission from proton beams

• Conclusions

Simulation Model

Solar surface

Magnetic Field Line

CME

Shock Wave

v

v

90°Model(1):90°

Model(2):90°

Simulation Model

• Two-dimensional fully relativistic electromagnetic Particle-In-Cell code.

• System size: Lx=800, Ly=10

• The free boundary condition in the x-direction, and the periodic boundary condition in the y-direction are imposed.

Initial Conditions and Parameters

0

x

y

E=v×B(Ez=vyBx)

B0v

10

200 8000

10

B=0n=4n0=400v=3vA=0.24c

B=B0

n=n0=100v=0

Mass ratio :mi=64me

Plasma beta :=0.05　　　　　 (ce/pe=0.632) ce:Electron cyclotron frequencype:Electron plasma frequency

Alfvén velocity :vA=0.08c

(c=light velocity)

Model(1)

Model(2)

Parameter Runs• Alfvén Mach (v/vA) : 3, 2, 1.5

• Propagation Angle () : 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°.

Wave Emission Process

0.3

0.2

0.1

0.0

0.4

0.2

0.0

-0.2450400350300250

0.60.40.20.0-0.2

0.60.40.20.0-0.2

8006004002000

Ex

vex/c

vix/c

Ex

x

x

(pet=0)

(pet=90)

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 electrostatic waves behind the shock.

Shock region

Particle Acceleration

-0.15-0.10

-0.05

0.00

0.05

-0.4

-0.2

0.0

0.2

0.4

450400350300250

3.0

2.0

1.0

0.08006004002000

3.0

2.0

1.0

0.0

ByBy

viz/c

vez/c

x

x (pet=0)

(pet=90)

Both electrons and ions arestrongly accelerated in the z-direction near the shock front

through the surfing mechanism.

Shock region

Surfing Acceleration byElectrostatic wave propagating perpendicular to magnetic field

€

midv

dt= e(E +

v

c× B)

Equation of Motion Ex=E0sin(t-kx)By=B0

x

y

z

e

€

vz = −v phωcit + v0z

Acceleration Factor

Solve for vz

In moving frame

Ex

€

E⊥B

≈ ρ i (c

ω pe)−1 VA

2

cvth, i(MA − 1)3 / 2

Vmax

VA≈ (mime

)1/ 2 (MA − 1)3 / 2

ω ci tA ≈ MA−1ω piω ci

Spatial Distribution of Ex and Ez Ex Ez

x x

(pet=18) (pet=66)0.03

0.02

0.01

0.00

-0.018006004002000

Red arrow area (x=70 〜 326) are used to find the dispersion relation of Ex.Blue arrow area (x=540 〜 796) are used to find the dispersion relation of Ez.

-0.04

-0.02

0.00

0.02

0.04

400300200100

Dispersion Relations of Ex and Ez

-4 -2 0 2 4

4

3

2

1

2.5 3.0 3.5 4.0 4.5

-4 -2 0 2 4

4

3

2

1

0

0 1 2 3 4 5

/pe

kc/pe

/pe

kc/pe

Ex Ez

Elecrostatic Langmuir Waves (Z-mode) are generated in theyellow contour line.

EM Waves areexcited.

• 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.

Conclusions

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.

1.Generation of magnetosonic shocks during collision of two current loops

Simulation System

• PIC simulation

• Force-Free magnetic configuration– J×B = 0 – Uniform density and uniform

temperatur

• System size:– 900× 900– n0=100 – Loop position ： (300, 300) & (600,

600)– Loop radius ： 100 200 400 600 800

800

600

400

200

x

y

€

Bθ =B0r1 /a

1+ (r1 /a)2+

B0r2 /a

1+ (r2 /a)2

Bz =B0

1+ (r1 /a)2±

B0

1+ (r2 /a)2

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Ç™Ç±ÇÃÉsÉNÉ`ÉÉÇ å©ÇÈÇΩÇflÇ…ÇÕïKóvÇ≈Ç∑ÅB

2.Generation of magnetosonic shock during formation of

current sheet



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.

Electron(solid line) and Proton(dashed line) velocity distribution:

(a) t=0 and (b) pet=1500



• 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).

Proton beams propagating into high density region



• 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.

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

• 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.

Shock formation and double structure(60 degree)

Time History of Ex and Ez

2x10-4

3

4

56

50454035302520

Ex Ez

pet pet

(Electrostatic) (Electromagnetic)

Parameters Red line: /pe=1.3 〜 1.6, kc/pe=0 〜 2.5Black line: /pe=1.5 〜 2.0, kc/pe=0 〜 3.0Blue line: /pe=2.5 〜 3.5, kc/pe=0 〜 4.0

Fundamental

Second harmonic

They are obtained by Inverse Fourier Transformationusing the data of dispersion relations.

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x10-5

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motivation

Documents

shock frontthrough

reflected electrons

fast magnetosonic shock

fast magnetic shock

surfing mechanism

solar radio bursts

electrostatic waves

dispersion relation