Embedded current sheet in the Earth’s magnetotail

1. Embedded current sheet in the Earth’s magnetotail A.A.Petrukovich, A.V.Artemyev, L.M.Zelenyi Space Research Institute, Moscow R. Nakamura Space Research Institute, Graz Outline 1. Thin embedded sheets are frequently observed 2. How sheets can be quantified ? 3. Embedded sheets in the magnetotail context 4. Implications for substorms

2. Вложенный токовый слой в хвосте магнитосферы A.A. Petrukovich, A.V. Artemyev, L.M. Zelenyi Space Research Institute, Moscow R. Nakamura Space Research Institute, Graz 1. Тонкие вложенные слои – характерный объект в хвосте 2. Количественное описание вложенных слоев 3. Вложенные слои в контексте плазменного слоя 4. Вложенные слои в контексте суббури

3. Observations ISEE-1,2:thin current sheet (with small Bz) is embedded in a thicker plasma sheet Mitchell et al, 1990, Sergeev et al, 1993 Cluster: Embedding: spatial scale of current is smaller than spatial scale of density Runov et al., 2006, AnGeo Asano et al 2005, GRL

4. Jmax=J0+Je, Je<<J0 Harris profile Je Be B0 Embedded sheet profile Harris sheet: Be and Je: He=Be/Je Embedded sheet: J0 and B0:H0=B0/J0 Total: Jmax, B0, Be Je<<J0 , Jeis not resolved by Cluster at distances 15-20 Re Jmax ~J0

5. Embedded sheet in theory Thin current sheets have typical thickness~ Larmor radius in boundary magnetic field B0 B0 is less definite: embedding is often created just adding background plasmas. essentially embedded sheet in thin anisotropic current sheet model by Zelenyi et al.

6. Cluster view on embedding Cluster 2001-2004 cases: thin (almost) horizontal single-peaked symmetric sheets

7. Cluster view on embedding Theory predicts thickness of the order of ion Larmor in B0! L=B0/J0~B0/Jmax

8. Cluster view on embedding: uncertainties 1. Large current densities are underestimated 3. Particle sorts add scatter 2. Small current densities are overestimated: J0~Je

9. Quantify embedded sheet 1. L0 ~ 1-3 * RL0 2. Range of B0 => J0 ~ B0^2 with larger B0 sheets are thinner! => Magnetic flux F0 ~ B0 * RL0 = pc/e/B0 * B0 = const (B0) - “quantum” flux Most of the flux is in wings but Harris sheet has infinite range! Make J=0 at finite Z “finite” Harris (Veltri et al 1998) F0=(0.5-2)B0*L0 ~ 1-5 *B0*RL0

10. Embedding in the magnetotail context Total plasma sheet flux Fe is much larger than F0 at 15-20 Re F0~ (1-5) * 0.02 Wb/m (4000 eV) << Fe ~ 0.5 Wb/m 10 times! • Extreme case smallest possible B0 so that J0 >= Je • B0/Be >= sqrt(F0/Fe) ~ .3-.25 • 2. Extreme case B0 ~ Be: if F0<<Fe • singular thin sheet in empty plasma sheet Drop all plasma from plasma sheet Or much smaller Fe~F0 At 15 Re – post-plasmoid plasma sheet ?

11. Minimum embedding is indeed B0 > 0.25-0.3 Be 8 of 10 cases of B0 > 0.5 Be are after tailward plasmoids! Example-> Embedding in the magnetotail context

12. Embedding in the magnetotail context Depleted magnetic flux in the post-plasmoid plasma sheet Hones, 1984

13. Embedding in the magnetotail context Distant tail Fe~F0 B0~Be Be – small thin sheets are almost Harris Middle tail Fe is growing to E Be is growing B0 and J ? Near tail Boundary When Bz ~ B0 1D approximation Is not valid

14. Embedding in the magnetotail context Embedding parameters in Tsyganenko models depend on tail stretching Latitude 70 used as boundary of PS

15. Implications for substorms • Criterion of being inside embedded sheet when considering onset flows: • in a regular quiet sheet: F0/Fe < 1/10 B0/Be ~ 1/3, => b0 ~ 10 • 2. Plasma sheet with embedding is thinner for the same Fe and Be • than Harris sheet (it contains more flux and less plasma): • Re_new = Re_harris * (1+aF0/Fe)/(1+aB0/Be) = Re_harris *0.9 • Leaving more space for increase of open magnetic flux even when Be=const • 3. Total cross-tail current I grows towards Earth and during growth phase, • but local current density J is controlled by embedding • where and why current density peaks (at onset)?

16. Implications for substorms 4. During growth phase embedded sheet intensifies. Flux is removed or plasma is removed to allow larger B0 Petrukovich et al, 2007 Sergeev et al, 1993

17. Implications for substorms 5. Stability Zelenyi et al model predicts instability zone related with Bz Burkhart, 1992, suggested for an embedded sheet The growth rate scales as B0/Be *(1- (B0/Be)2)

18. Conclusions • Thin ion scale embedded sheets are frequent especially during substorms • Thickness is controlled by local larmor (as in theory) and plasma properties • Crucial internal parameter is B0, magnetic flux is constant. • Sheet in the magnetotail is controlled by B0/Beand F0/Fe • Quiet sheets have deep embedding B0<< Be (at 15-20 Re) and slowly • evolve with increase of B0 during growth phase Largest embedding B0~Be requires plasma sheet magnetic flux drop – • after onset or in the distant tail • Plasma sheet is thinner when embedded and less stable. • Embedding should be taken into account in analyses of ion kinetics, • global convection, stability, etc.