Concentrated Generator Regions Observed by Concentrated Generator Regions Observed by Cluster in the Plasma Sheet Boundary Layer:Cluster in the Plasma Sheet Boundary Layer:

2. Theoretical Considerations2. Theoretical Considerations

O. Marghitu (1, 2), M. Hamrin (3), B.Klecker (2),O. Marghitu (1, 2), M. Hamrin (3), B.Klecker (2),K. Rönnmark (3), A. Vaivads (4)K. Rönnmark (3), A. Vaivads (4)

(1) Institute for Space Sciences, Bucharest, Romania(1) Institute for Space Sciences, Bucharest, Romania

(2) Max-Planck-Institut für extraterrestrische Physik, Garching, Germany(2) Max-Planck-Institut für extraterrestrische Physik, Garching, Germany

(3) Department of Physics,(3) Department of Physics, Umeå University, Umeå, SwedenUmeå University, Umeå, Sweden

(4) Swedish Institute of Space Physics, Uppsala, Sweden(4) Swedish Institute of Space Physics, Uppsala, Sweden

Solar - Terrestrial Interactions from Microscale to Global ModelsSolar - Terrestrial Interactions from Microscale to Global Models ,, Sinaia Sinaia, September 7, , September 7, 20052005

A. Generator ingredients

B. Energy and work: Equations

C. Data: Qualitative evaluation

D. Data: Quantitative estimate

E. Summary and prospects

Outline

A Generator Ingredients A

CGR1 CGR2 CGR3 CGR4 CGR5

EYJY

EY

JY

PK

PB

PT

VX

VY

VZ

WK,WB,E•J

dV/dt = –PK+J×B | • V (1)

d(V2/2)/dt = –PK • V + (J×B) • V = WK + WL (2)

With d/dt = /t + V• and /t + •V = 0, Eq. (2) writes: (3)

E / t = – •(E V) + WK + WL , where E= V2/2 (4)

WL = (–V×B)•J = (E-E0) •J = E•J-E0•J ≈ E•J (5)

(J×B) = (×B)×B/0 = –PB + •TB , PB=B2/20 and (TB)ij=BiBj/0

=> WL= –V•PB + V• (•TB) = WB+WT (6)

•S = – ∂PB/∂t – E•J , S=E×B/0 (7)

B Energy and Work: Equations B

C Data: Qualitative Evaluation C

EYJY

EY

JY

PK

PB

PT

VX

VY

VZ

WK,WB,E•J

CGR1 CGR2 CGR3

C Data: Qualitative Evaluation C

EYJY

EY

JY

PK

PB

PT

VX

VY

VZ

WK,WB,E•J

CGR4 CGR5

CGR1 CGR2 CGR3 CGR4 CGR5

D Data: Quantitative Estimate D

Substantial Earthward directed Poynting flux during CGR1 => we select it for a quantitative estimate.

D Data: Quantitative Estimate D

EYJY

EY

JY

PK

PB

PT

VX

VY

VZ

WK,WB,E•J

CGR1

E/t= –•(E V)+WK+WL (4)• n<1cm-3, V<100km/s => E<10-11J

WK+WL 10-12

• E/TWK+WL => T 10s (small)

• EV/L WK+WL => L 1000km

WL=WB+WT E•J (5, 6)• E•J –2 10-12, WB –6 10-12

=> WT 4 10-12 W/m3

WT = V• (•TB) VB2/0L (6)

• B=30 nT, V=50 km/s=> L 10,000 km

D Data: Quantitative Estimate D

The Poynting theorem: •S = – ∂W/ ∂t – E·J (7) with WWB=B2/20 PB. ∂ / ∂t d / dt in the satellite system, because Vsat << Vplasma. In panel (e) => regions where – dPB/ dt >0. Both terms on the r.h.s. of (7) positive => elmag. energy carried away from the CGR. – ∂PB/ ∂t 0.2nPa / 200s = 10-12W/m3, comparable to –E·J.

EYJY

EY

JY

PK

PB

PT

VX

VY

VZ

WK,WB,E•J

CGR1

Good correlation between E•J<0, WK>0, and WB<0.

The thermal pressure forces push the plasma element (PE)

against the magnetic pressure, consistent with energy conversion.

The magnetic tension does work on the PE, WT>0.

CGRs have a scale size of a few 1000km, consistent with

estimates based on conjunction timing and energy flux mapping.

In at least one case Poynting flux is leaving the CGR.

In this case the decrease in the magnetic energy and the

conversion term, E•J, make comparable contributions to •S.

E Summary E

Better evaluation of PK, by using PK+PB=const. on SC2

Computation of WT by direct evaluation of •TB.

Direct evaluation of •S.

E Prospects E