Particle acceleration and plasma heating in the chromosphere

Alexander Stepanov ,

Pulkovo Observatory, St.Petersburg, Russia

Valery Zaitsev

Institute of Applied Physics, N.Novgorod, Russia

Prague “Solar and stellar Flares”June 23-27, 2014

OUTLINE OF TALK

• BBSO New Solar Telescope : in situ choromosphere heating• Rayleigh-Taylor instability: General• Particle acceleration mechanism by induced electric field• Chromosphere heating mechanism (collisions)

Consequences:• Plasma radiation at sub-THz from chromosphere• Origin of sub-THz pulsations: Electric circuit model• Electric current diagnostics• Deja vu – come back to the ‘chromospheric flare’.

Haisheng Ji et al. (ApJ Lett 2012): In situ chromosphere heating to T ≥ 106 K.

Observation of Ultrafine Channels of Solar Corona HeatingHaisheng Ji et al. 2012 ApJ 750 L25

Indications on chromosphere heating in situ

Sharykin & Kosovitchev (ApJ 2014):

BBSO observations reveal previously unresolved sub-arcsecond structure of the flare ribbons consisting from numerous small-scale (≤ 100 km) bright knots.Plasma is heated to high temperature by some another mechanism different from thick-target model. I ≈ 5×1010 A. Joule heating?

Rayleigh-Taylor instability(Carlyne et al. ApJ 2014)

Rayleigh-Taylor Instability (Ballooning mode) in Corona and Chromosphere

Prominence at the loop top

Fp=ρg

Fc= 2nTRc/Rc2

18

2 2

20

ga

tV

Tnn

nT

ea

)(

)(

Instability condition:

Ballooning Instability in a Current-carrying Magnetic

Loop

TT

x

xnn a5

5.0182 10185.1

583.6exp102.71

)(

To determine the temperature to which the chromosphere should be heated we used a modified Saha formula:

KKKT 444 102.1,105.1,102 3141516 10,10,10 cmnnn atotfor

Current dissipation is provided by the Cowling conductivity related to electron-atom collisions.

2

2'

)1(

)1(

x

xVnmq riai

J

The radiation losses

nnnTq ar )()10397.1( 15.68

From qj > qr we obtain the lower boundary for the rate of photosphere convection that provides pre-heating: scmVr /105,3 4

Induced electric field in a current-carrying loop

Before R-T Instability:

Penetration of chromosphere plasma into a loop with velocity

From Eqs and

No acceleration!. But for the time s a disturbance dealing with is running away from instability domain as a non-linear

Alfven wave: E || Bz appears and particle

acceleration is realized in the electric field for

E ≈ 0.1 V/cm and the electron energy is about Є ≈ 1 MeV.

.)( constrBz 0 arBrB /)( 00

artVtrV rr /)(),(

}[ BVrott

B

t

B

cErot

1 ])[/1( BVcE

255 AA Vl /

),( trB

04 2

220

2

2

z

BB

t

Bz

lc

VIE A

z 20

3

AIcmlGBcmna9

072316 105105110310 ,)(,,

Particle Acceleration & Chromosphere Plasma Heating

• Disturbance of electric current in flare loop

due to ballooning instability. Electric field generation.

• Electron acceleration by induced Е-field.

• Heating of chromosphere plasma by

accelerated electrons.

• Accelerated particles don’t leave the source and lost energy completely.

• Plasma heating rate by fast particles(Knopfel & Spong, 1979):

• Radiation losses qr < qs for ED/Ez ≈ 40,ED is Dreicer field.

сmVlrc

IlVE r

z /10)51( 2

12

01

keVlEz 10005001s

Particle mean free path:

сmne

siieiee

74

2

1052

1l

z

D

z

D

z

Deiss E

E

E

E

E

Enq

4

2exp35,0

8/3

)105(10 62/1219 KTTnqr

FLARING LOOP

Ballooning instability

THz- source

“Transparency” conditions for chromosphere:

- Large currents in flaring loops ~1011 A

- Ballooning instability, which induced electron acceleration in the chromosphere, plasma heating and plasma wave turbulence generation.

Even for В = 2000 G ωp/ ωсe ≈ 40 >>1.

So, isotropic plasma approximation is

true.

keVсmn

KTсmn

s 1000500,10

,10103,105

s39

76314

Requirements to the source:

eips

n

n 610n

ns

Consequences: Plasma radiation in sub-THz (Sakai et al. 2006; Zaitsev, Stepanov, Melnikov, 2013)

Conversion l→ t: Radiation at the fundamental (ω = ωp ) and harmonic ω = 2ωp = (4π)×200 GHz

Tb2 ~ (nT)w2 w = Wpl/nT

extextextcnb Ta

T

exp1expexp1

“Transparency” at plasma turbulence level w ≥ 10-4

w

mm

TT

ne

ib

73

11

105.1exp106

1)exp(3

Maser-effect μ < 0:

Solar plasma radiation:

at sub-THz

at MHz-GHz

Challenge in solar physics: > 104 sfu emission at 212 and 405 GHz with pulsations (Kaufmann et al. 2004, 2009).

Pulsations with modulation depth 5-8% and periods 0.2-4 s.

Consequences: Pulsations at sub-THz from solar flares (Zaitsev, Stepanov, Kaufmann, SP 2013)

Puzzling proportionality between pulse repetition rate and mean emission fluxes

We suggest electric circuit model (RLC) for QPPs

Modified Alfven oscillations: νRLC = VAφ/r – that is RLC-pulsations with к

almost perpendicular to В (cosθ = Bφ/Bz << 1).

Flare trigger: – plasma tongue driven by ballooning instability

Current in the flare I ≈ 1011 A.

Let us determine L, C, R и Q:

L ≈ 10l = 1010 сm = 10 Henry; С = (с2/VA2)S/l ≈ 1011 сv = 0.1 F.

Period Р = √LC ≈ 1 с.

Q-factor Q = R-1(L/C)1/2 Reff = W/I 2 = 1018 W/1022 А2 = 10-4 Ohme.i. Q ≈ 3×104 >> 1

Coronal loop as an equivalent RLC-circuit

For small current deviation → the equation of a linear oscillator (Khodachenko et al 2009):

Excitation:

Oscillation frequency

Quality factor

II ~

44

22

4rnmc

lIR

ia

4

78ln4

r

llL

310/1 CL

cRQRLC

0)(

~~||)(

~

21

2

2

ICI

tI

crlV

IRtI

cL r

2

2

2

24

,2 A

AAi

c

c

l

S

lI

SnmcC

)/(||)( 21 rclVIR r

imncr

I

ILC

c

22

2

0

210

02

1

/)()(

Diagnostic of electric current in a flare using pulsations at sub-THz

From pulse rate variation in the flare on 4 November 2003 (Kaufmann et al. ApJ, 2009) a decrease of the electric current from 1.7×1012А in the flare maximum to 4×1010А after the burst was found.

imncr

I

ILC

c

22

2

0

210

02

1

/)()(

Conclusions

Rayleigh-Taylor instability plays important role in particle acceleration and plasma heating in deep layers of the solar atmosphere.

Deja vu – back to the ‘chromospheric flare’ (Ŝvestka,Fritsova- Ŝvestkova)

Coronal flares ate also possible

To comprehend physics of solar chomosphere flares more multi-wavelength observations including THz band are needed.

Thank you