IMF derivation from Pickup Ions observed by ASPERA UT UT UT M. Yamauchi B ion ion motion in velocity space is a ring! (spiral motion in real space)

In-coming directions of ions Azimuth scan  Elevation scan  Electric scan IMA

Ion motion with V 0 =0 Viewing from +B Viewing from +E Initial  velocity to B is V 0 cos  velocity space trajectory V* X VYVY VXVX V* Y V* Z VZVZ V (SW frame) = V* (Martian frame) + V SW B 3-D view Ring  2D  minimum variance direction (N) is parallel to B! V 0 =0 in Martian frame means V 0 = -V SW in SW rest frame where E=0.  simple spiral motion,  ring trajectory in velocity space.

, ELS (ch8) + IMA  = 5~15  = 4  = 3  = 2  = 1 SW ring MEX orbit (light blue) during UT in the cylindrical MSO coordinates. R 2 = Y 2 +Z 2. average IMB average BS Mars

Distribution in velocity space MSO (XYZ) MVM (LMN)

Manual method vs. Automatic method Manual Automatic

However, IMA orientation is not always ideal UT All ch8

Aligned in the azi-direction (points 2, 3, 4, 5)  Linear alignment (small data range in M direction) IMA IMA light ion (H+ and He++), 3~8 keV  =5~14  =15  =1  =2  =3  =4 Viewing from +B Viewing from +E

general V 0 ≠0 case  MAX Minimum variance method gives clear L direction (// ±E), but not M & N directions.  We may not use ±N as estimate of B direction, but (1) E x V SW gives B Y /B Z orientation ! (2) B X /B (or  ) can be obtained intuitively

Check item (1) Alignment direction of the ring data by IMA ≈ Maximum variance direction (L X, L Y, L Z ) where L X << 1  B T =(0, B Y, B Z ) // V SW x E // (0, L Z, -L Y ) (2) Sign of B : If L = evolution direction, then sign(B Z ) = - sign(L Y ) (3) Tilt toward X (=  ) *  ' = angle between max energy (  MAX ) direction and SW direction * Ratio k = V MAX /V SW = (  MAX /  SW ) 1/2 If V 0 = 0, two angles must be the same, i.e.,  ' = , and k = cos(  )  If cos(  ') = k, most likely  =  '

Result Using (3)~(6)  Changing IMF for event 0608 UT, northward IMF, X tilt ~ +35~40°, Y tilt ~ -10° 0613 UT, northward IMF, X tilt ~ +35°, Y tilt ~ -45° 0623 UT, northward IMF, X tilt ~ +20°, Y tilt ~ -30° 0633 UT, X tilt > +40° Using (1)~(2)  Constant IMF for event UT, dawn-dusk oriented IMF, X tilt ~ 20°

Procedure (1) Manually select the ring distribution. (2) Apply the minimum variance method to determine L, M, and N. If the ring data is well arranged into a partial circle, ±N // B If not, (3) Examine |L X | < 0.3. If yes, L // -E SW. If not, remove the direction that corresponds to the lowest energy from the selected set of data and re-calculate a new L. (4) Manually obtain  MAX and  '. (5) Check if  MAX /4  SW ≈ cos 2 (  ') is satisfied. If yes, we have  ≈  ', where B X /|B| = sin(  ). (6) If possible, identify the evolution direction and determine the sign of L and E SW. B T is parallel to V SW x E SW.

Summary Approximate IMF orientation can be derived from ring-like distributed protons as measured by the IMA. The actual derivation of the ring plane is complicated (see procedure) due to the very limited viewing directions and angular resolution of the instrument.

New work (1) Beam ? event

New work (2) Use magnetosheath event (again) Can we obtain "sign" of B direction?

H+ only (no He++) !  = 3  = 2  = 4  = 3  = 2 SW He ++ Ring H + SW H +

Motion of ring ions Ion motion with V 0 =0 velocity space trajectory V* X VYVY VXVX V* Y V* Z VZVZ V (SW frame) = V* (Martian frame) + V SW B 3-D view

(easy case)

Beam-origin (V 0 ≠ 0) ring distribution

Selected ring data : ~ 1344~1347 UT *1) L = (0.05, -0.02, 1.00) in MSO *2) M = (0.94, -0.34, -0.06) in MSO *3) N = (0.34, 0.94, ) in MSO

Aligned in azimuthal direction  Almost 1-D alignment  Difficult to determine ring "plane"

From ring data at ~0623 UT ( ) V L (km/s) V N (km/s) V M (km/s)

Selected ring data : ~ 0608 UT *1) L = (0.06, 0.99, 0.14) in MSO *2) M = (0.79, 0.04, -0.61) in MSO *3) N = (0.61, -0.15, 0.78) in MSO

Beam-origin Alignment direction of the ring data by IMA ≈ Maximum variance direction (L X, L Y, L Z ) where L X << 1  B T =(0, B Y, B Z ) // V SW x E // (0, L Z, -L Y ) Sign of B If L = evolution direction, sign(B Z ) = - sign(L Y ) Tilt toward X (=  ) *  ' = angle between max energy (  MAX ) direction and solar wind direction * Ratio k = V MAX /V SW = (  MAX /  SW ) 1/2 If V 0 = 0, two angles must be the same, i.e.,  ' = , and k = cos(  )  If cos(  ') = k, most likely  =  '  MAX