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

1. Concentrated Generator Regions Observed by Cluster in the Plasma Sheet Boundary Layer: 2. Theoretical Considerations O. Marghitu (1, 2), M. Hamrin (3), B.Klecker (2), K. Rönnmark (3), A. Vaivads (4) (1) Institute for Space Sciences, Bucharest, Romania (2) Max-Planck-Institut für extraterrestrische Physik, Garching, Germany (3) Department of Physics,Umeå University, Umeå, Sweden (4) Swedish Institute of Space Physics, Uppsala, Sweden Solar - Terrestrial Interactions from Microscale to Global Models, Sinaia, September 7, 2005

2. Outline • Generator ingredients • Energy and work: Equations • Data: Qualitative evaluation • Data: Quantitative estimate • Summary and prospects

3. SEYJY EY JY PK PB PT VX VY VZ CGR1 CGR2 CGR3 CGR4 CGR5 WK,WB,E•J A Generator Ingredients A

4. B Energy and Work: Equations B  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 = – •(EV) + 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=B2/2m0 and (TB)ij=BiBj/m0 => WL= –V•PB + V•(•TB) = WB+WT (6) •S = – ∂PB/∂t – E•J , S=E×B/m0(7)

5. SEYJY EY JY PK PB PT VX VY VZ WK,WB,E•J C Data: Qualitative Evaluation C CGR2 CGR3 CGR1

6. SEYJY EY JY PK PB PT VX VY VZ WK,WB,E•J C Data: Qualitative Evaluation C CGR4 CGR5

7. D Data: Quantitative Estimate D CGR1 CGR2 CGR3 CGR4 CGR5 • Substantial Earthward directed Poynting flux during CGR1 => we select it for a quantitative estimate.

8. SEYJY EY JY PK PB PT VX VY VZ WK,WB,E•J CGR1 D Data: Quantitative Estimate D • E/t= –•(EV)+WK+WL(4) • n<1cm-3, V<100km/s => E<10-11J • WK+WL  10-12 • E/TWK+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/m0L (6) • B=30 nT, V=50 km/s • => L  10,000 km

9. SEYJY EY JY PK PB PT VX VY VZ WK,WB,E•J D Data: Quantitative EstimateD • The Poynting theorem: •S = – ∂W/ ∂t – E·J (7) with WWB=B2/20 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. CGR1

10. E Summary E • 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.

11. E Prospects E • Better evaluation of PK, by using PK+PB=const. on SC2 • Computation of WT by direct evaluation of •TB. • Direct evaluation of •S.