# Presentation: 204503

## TOPIC 1:  HALL MHD EFFECTS IN THE MAGNETOSPHERE

- TOPIC 2:  MEASURING RECONNECTION RATES IN THE MAGNETOSPHERE
- TOPIC 3:  ELECTRON DIFFUSION REGION OBSERVATIONS IN THE MAGNETOSPHERE

- Forrest Mozer
- Space Sciences Laboratory
- University of California, Berkeley

## RECONNECTION

**     ****Reconnection is the process that occurs when magnetized plasmas flow**
**     ****into each other.  It produces**
**a.  Change of topology**
**b.  Particle acceleration**
**      ****Reconnection occurs at the magnetopause, on the sun, on all scales in astrophysics (accretion disks, etc.) and in laboratory plasmas.**

**RECONNECTION**

## BACKGROUND

**E**+**U**ex**B **= c******·**Pe/en + (mec2/ne2)**j**/t + **j**

**E**+**U****I**x**B **= c**j**x**B**/en c******·**Pe/en + (mec2/ne2)**j**/t + **j**

- THE GENERALIZED OHM’S LAW

- Resistive MHD    Include only last term on the right side
- Hall MHD            Also include c**j**x**B**/en on the right side

- Ions are demagnetized (don’t move with the **E**x**B** velocity)
- Ion scale size ~c/ωpI ~ 150 km at sub-solar magnetopause
- No parallel electric field, so no reconnection in ion region
- Electrons move with **E**x**B** velocity
- From simulations and lab, expect quadrupolar B and bipolar E

- Electrons are demagnetized by terms on the right side
- Electron scale size ~c/ωpe ~ 4 km at sub-solar magnetopause
- Parallel electric field, so reconnection occurs

## Cluster Encounter with the Diffusion Region in the Magnetotail on 2003-09-19

-  Clear detection of Hall electromagnetic fields
- - Large electric fields in density minima in the 	        vicinity of separatrices

- Quadrupolar
- magnetic field

- Bipolar
- electric field

## Context:
Reconnection jet (Vx) reversal
Normal magnetic field (Bz) reversal
Clear evidence for Hall electric field

- Reconnection jet (Vx) reversal
- Normal magnetic field (Bz) reversal
- Clear evidence for Hall electric field

- Borg et al, GRL, 2005

- *
- *
- *

## QUADRUPOLAR BY                    BIPOLAR EZ

- Hall By negative
- Hall By positive

- QUADRUPOLAR BY                    BIPOLAR EZ

## Large electric fields associated with density minima at separatrices

## Wygant et al, JGR, 2005

## Slide 9

## ION ACCELERATION ON THE ION SCALE

## Slide 11

## Slide 12

## POLAR SUB-SOLAR OBSERVATION OF THE ION SCALE

## COMPARISON OF COMPUTER SIMULATION AND MAGNETOPAUSE DATA

## COMMENTS

- Classic crossing near 0547
-         sheath  sphere
- 2.  Another crossing near 0552
-         sphere  sheath
- Hall MHD fields very
-         different on 2nd crossing
- Second crossing because
-         (ExB)X changed
- Post-reconnection flow
-         towards x-line

## Slide 16

## Slide 17

## Slide 18

## Dimensionless Reconnection Rate = Bnormal/Btotal

**MEASURING THE RECONNECTION RATE IN THE MAGNETOSPHERE**
**RESULTS:  ~6 determinations in the magnetosphere, all with dimensionless**
**                       ****reconnection rates ****≤0.1.  These results are VERY uncertain.**

- Dimensionless Reconnection Rate = Bnormal/Btotal
-                                                     or = (Etangential/B)/valfven

- To measure the dimensionless reconnection rate, one must:
-                  a) be in the frame of the moving current sheet.
-                  b) know the normal direction accurately.

- This is often done by:
-               Minimum Variance analysis of B
-               Maximum Variance analysis of E
-               Faraday Residues method that uses both B and E

- These methods assume:
-              Steady state (no δ/δt)
-              Boundary is planar and moves at constant speed
-              Data has no uncertainties.
-  THIS MAY NEVER HAPPEN

## EXAMPLE OF THE MEASUREMENT OF THE RECONNECTION RATE ON CLUSTER 

- (this may become the most accurate measurement to date)

- ADVANTAGES OF CLUSTER:
-   Four spacecraft: measure boundary speed by timing crossings
-   In 2002, separations of the spacecraft were ~100 km ~ c/ωpI
-        Effects of non-planar boundary and δ/δt ≠ 0 are minimized

- PROCEDURE
- Low pass filter the data.
- Transform to the frame moving at the boundary speed.
- Maximum Variance analysis on the electric field to obtain the normal to the boundary.
- Rotate about this normal to maximize the variance of the magnetic field in the tangential plane.

## MAGNETOPAUSE CROSSING OF MARCH 30, 2002

- Spacecraft trajectory

- SUN

- Lobe

- Magnetosheath

- Crossing very near X-line because diffusion region width was ~c/ωpI
- BZ changed from negative to positive and density increased

## Cluster SC2, March 30, 2002

-        NOTES:
- Reconnection B goes from -140 to +70 nT.
- Guide field ~ -50 nT
- Normal B varies but
- average is -3.4 nT.
- Reconnection rate
- ~ 3.4/100 = 0.034
- Because of time variations, this estimate is uncertain

## Cluster SC2, March 30, 2002

##       NOTES:

- Cluster SC2, March 30, 2002

-       NOTES:
- EX has bipolar Hall MHD signature
- Tangential (EY and EZ) components vary but
- <EY> = 0.3
- <EZ> = -1.25

## Cluster SC2, March 30, 2002

- NOTES:
- Z-flow negative in center because SC south of the x-line.
- Z-flow positive in sheath because of solar wind flow over the magnetosphere.
- X-flow >0 early and <0 late, so flow towards the diffusion region from both sides

## THE DIMENSIONLESS RECONNECTION RATE FROM THE ELECTRIC FIELD MEASUREMENT

- AVERAGES:
-   First second    0.003
-   Last second   -0.046
-   BN/BTOTAL gave 0.034
- RESULT: 0.028±0.013

- NOTES:
- Reconnection  rate is determined by asymptotic values,
- not the values in the diffusion region..
- It is negative at
- the end because the EXB flow is in the
- –X direction.

##                                   CONCLUSIONS

- Hall MHD effects (quadrupolar magnetic field and bipolar  electric field) exist in the magnetosphere.
- 2. They occur more often (?) in the tail than in the sub-solar region.
- 3. They occur for symmetric geometries (near-constant density and equal and opposite reconnection magnetic fields) with B approaching zero in the current sheet.
- 4. They occur infrequently (≤1% of the time in the sub-solar region).  WHY?  LAB EXPERIMENTS AND SIMULATIONS CAN HELP ANSWER THIS QUESTION.
- 5. The reconnection rate is difficult to measure.  The March 30,2002 event may become the best example yet found (four spacecraft with two measurements/spacecraft).

## SYMMETRIC, 2-D MODEL OF MAGNETIC FIELD RECONNECTION

- Electron
- Diffusion Region

-             COMMENTS
- Two scale sizes
- In the real world, this geometry occupies a volume having a measure of zero.
- Two classes of electron diffusion regions.

- Separatrix