Coronal ion-cyclotron beam instabilities: a multi-fluid description

1
Coronal ion-cyclotron beam instabilities a
multi-fluid description

• Redouane Mecheri

Max-Planck Institute for Solar System Research
EGU meeting, Vienna, 20 April 2007
2
Outline

• Introduction Ion-cyclotron waves in the corona
• Multi-fluid model, local and non-local
  (ray-tracing) linear modes analysis
• Results
• Ion-cyclotron waves
• Ion-cyclotron beam-instabilities
• Summary and conclusions

Redouane Mecheri, EGU meeting, Vienna 20 April 2007
3
The solar corona
Coronal hole
Quiet region
Active region
Yohkoh X-Ray image
Redouane Mecheri, EGU meeting, Vienna 20 April 2007
4
Heavy ions anisotropic heating in the corona
Redouane Mecheri, EGU meeting, Vienna 20 April 2007
5
Ion-cyclotron waves and anisotropic heating
Cyclotron motion of an ion around the B-field
Ion-cyclotron wave propagating along the B-field
Courtesy S. Cranmer
Redouane Mecheri, EGU meeting, Vienna 20 April 2007
6
Origin of the ion-cyclotron waves

• Small scales reconnection events ? heating,
  plasma outflow and high-
• frequency waves (10 Hz to 1 kHz)
• Turbulence cascade of low-frequency large scales
  MHD waves
• towards high-frequency small scales waves
• Reflection and refraction of MHD waves ?
  conversion to smaller
• scales high-frequency waves
• The coronal plasma tenuous, collisionless,
  non-uniform ? ideal for
• developing micro-instabilities ? excitation
  of high-frequency waves

Redouane Mecheri, EGU meeting, Vienna 20 April 2007
7
Motivations

• Effect of a second population of ions the
  corona is naturally multi-species
• Particles accelerated from small scales
  reconnection event beam
• particles ? beam-type micro-instabilities
• MHD is a large scale one-fluid description of
  the plasma with very low
• frequencies, i.e. ? ltlt ?i

Redouane Mecheri, EGU meeting, Vienna 20 April 2007
8
Outline

• Introduction Ion-cyclotron waves in the corona
• Multi-fluid model, local and non-local
  (ray-tracing) linear modes analysis
• Results
• Ion-cyclotron waves
• Ion-cyclotron beam-instabilities
• Summary and conclusions

Redouane Mecheri, EGU meeting, Vienna 20 April 2007
9
Collisionless multi-fluid model

• Mass continuity equation ? mass conservation

• Momentum equation ? force balance

• Energy equation ? energy balance

• Maxwell equations ? electromagnetic field

Redouane Mecheri, EGU meeting, Vienna 20 April 2007
10
Working assumptions

• Isotropic pressure (for simplicity)
• Mass-less electron ? electron inertia neglected,
  time-scales of interest of the order of the ion
  gyro-period
• Collisionless plasma, i.e. ?iltlt ?ei
• Displacement current neglected in Amperes law
  (no relativistic effects)
• WKB assumptions, i.e. ? ltlt L ? slowly varying
  medium

Redouane Mecheri, EGU meeting, Vienna 20 April 2007
11
Linear perturbation analysis
Redouane Mecheri, EGU meeting, Vienna 20 April 2007
12
Background plasma configuration

• 2D analytical funnel
• model of Hackenberg
• et al. 2000 (current free).

Redouane Mecheri, EGU meeting, Vienna 20 April 2007
13
Outline

• Introduction Ion-cyclotron waves in the corona
• Multi-fluid model, local and non-local
  (ray-tracing) linear modes analysis
• Results
• Ion-cyclotron waves
• Ion-cyclotron beam-instabilities
• Summary and conclusions

Redouane Mecheri, EGU meeting, Vienna 20 April 2007
14
Plasma configuration
0
no free energy stored in the plasma
Plasma initially at rest

• quadratic polynomial
• ? real ? stable mode

Redouane Mecheri, EGU meeting, Vienna 20 April 2007
15
Two-fluid (e-p)
x8.5 Mm, z2.5 Mm, ? 82?

• Additional ion-cyclotron mode (IC2)
• Additional slow mode (SM2)

Redouane Mecheri, EGU meeting, Vienna 20 April 2007
16
Outline

• Introduction Ion-cyclotron waves in the corona
• Multi-fluid model, local and non-local
  (ray-tracing) linear modes analysis
• Results
• Ion-cyclotron waves
• Ion-cyclotron beam-instabilities
• Summary and conclusions

Redouane Mecheri, EGU meeting, Vienna 20 April 2007
17
Beam particles from small scales reconnection
events
Plasma flow with typical velocities of 100 to 300
km/s at 1.5-2 Mm.
SUMER/SOHO Si IV 1.393-Å line spectral
observations of explosives events in the
chromospheric network at 1.5-2 Mm (Innes et al.,
Nature 1997).
Beam particles
Redouane Mecheri, EGU meeting, Vienna 20 April 2007
18
Beam plasma configuration
streaming of plasma species j
free energy provided to the plasma

• non-quadratic polynomial
• ? complex ? instability

Redouane Mecheri, EGU meeting, Vienna 20 April 2007
19
Alpha (He2) beam
x 8.5 Mm, z 2.5 Mm, ? 82, n? 0.1 np , ?
20
Redouane Mecheri, EGU meeting, Vienna 20 April 2007
20
Alpha (He2) beam
x 8.5 Mm, z 2.5 Mm, ? 82, n? 0.1 np , ?
20
Redouane Mecheri, EGU meeting, Vienna 20 April 2007
21
Left-hand resonant instability
x 8.5 Mm, z 2.5 Mm, ? 82, n? 0.1 np,
VAp150 km/s
Redouane Mecheri, EGU meeting, Vienna 20 April 2007
22
Alpha (He2) beam
x 8.5 Mm, z 2.5 Mm, ? 82, n? 0.1 np , ?
70
Redouane Mecheri, EGU meeting, Vienna 20 April 2007
23
Alpha (He2) beam
x 8.5 Mm, z 2.5 Mm, ? 82, n? 0.1 np , ?
70
Redouane Mecheri, EGU meeting, Vienna 20 April 2007
24
Right-hand resonant instability
x 8.5 Mm, z 2.5 Mm, ? 82, n? 0.1 np,
VAp150 km/s
Redouane Mecheri, EGU meeting, Vienna 20 April 2007
25
Resonant instabilities
x0 6.5 Mm, z0 2.5 Mm, ? 0 78
Left-Hand
Right-Hand
Redouane Mecheri, EGU meeting, Vienna 20 April 2007
26
Summary and conclusions

• Ion-cyclotron waves
• Extension of slow (S), Alfvén (A) and fast (F)
  MHD modes to ? ?i
• Consideration of He2 ? appearance of cut-off and
  mode conversion with additional slow and
  ion-cyclotron mode
• Ion-cyclotron beam instabilities
• left-hand resonant instability important at
  highly oblique propagation
• right-hand resonant instability important at
  quasi-parallel propagation
• affected by the B-field geometry, can propagate
  to the upper part of the funnel with however a
  rapidly decreasing growth rate to a zero value.

Redouane Mecheri, EGU meeting, Vienna 20 April 2007
27
Thank you for your attention
Redouane Mecheri, EGU meeting, Vienna 20 April 2007