1. Mass-loading effect in the exterior cusp and plasma mantle
M. Yamauchi1 and R. Slapak2
1. Swedish Institute of Space Physics (IRF), Kiruna
2. Luleå University of Technology (LTU), Kiruna
Poster (EGU ), Wednesday ( )

2. What is mass-loading? mSWnSWUSW + mionnionUion = mSWnSWUinitial
Slow down of collision-free plasma flow (normally solar wind) after mixing with newly appeared plasma (normally planetary/cometary heavy ions) into that flow, as a result of conservation of total momentum.
mSWnSWUSW + mionnionUion = mSWnSWUinitial
The transferred momentum from the decelerated inflow is given to the acceleration of the mixing plasma, and the acceleration part have been modeled by ion pickup process, through the convection electric field (Figure 1). In the ion pickup process, momentum transfer continues until the average velocity (guiding center velocity) of the mixing plasma reaches the same velocity as the solar wind (i.e., until Uion = USW). Assuming mion/mSW = 16 (mass ratio of O+ and H+), we have
[1 + 16·(nion/nSW)]·Ufinal = Uinitial (1)

3. “Traditional” pickup ion motion
Linear approximation: Energy is converted to gyromotion, but not to E 3

4. How about kinetic energy?
Since the process is not elastic (two species finally move together), conservation of momentum means loss of total kinetic energy of the bulk flow. From equation (1), the total kinetic energy (K) after the completion of the mass loading (ion pickup) process is calculated as:
Kfinal = mSW(nSW+16·nion)Ufinal2/2= mSWnSWUfinalUinitial/2 or
[1 + 16·(nion/nSW)]·Kfinal = Kinitial (2)
Thus, kinetic energy decreases by the same factor of [1 + 16·(nion/nSW)].

5. Mass Loading at Earth: cusp & Mantle
~ 10 cm-3 solar wind (H+) inflow to the exterior cusp
~ 0.1 cm-3 outflowing O+ in the exterior cusp / plasma mantle
(1) and (2)  Up to 14% loss of total kinetic energy

6. Where does the kinetic energy go?
If the pickup ion starts from zero velocity (comet/Mars case), this energy is expected to be converted to gyromotion (thermal energy) in linear approximation and charge separation (modification of the electric and magnetic fields) for non-linear case. Rosetta ion data shows that non-linear effect more than expected (Behar et al., 2017).
 Conversion to electrostatic energy must not be ignored even zero initial velocity.
For the Earth's case (Figure 2), mass-loading O+ is already heated (occupying all gyro-phase), and the kinetic energy cannot be converted to the thermal energy  We expect powering to dynamo (electrostatic energy) [Yamauchi and Lundin, 1997]
Yamauchi and Lundin [1997] predicted such effect in their cusp model, but O+ excape rate was not clear at that time. Now, Cluster data gives good estimate of such effect (Figure 3).

7. Simple calculation Vfinal/VSW Power (W/km2)1
0.8
0.6
0.4
0.2
Vfinal/VSW
With 0.1 cm-3 O+ mixing to 10 cm-3 incoming flow with 100 km/s velocity, this power reaches up to 3 W/km2, which is sufficient in powering the cusp current system and relevant ionospheric convection.
Simple calculation 8 7 6 5 4 3 2 1
Power (W/km2)
O+ density [cm-3] (into 10 cm-3 SW inflow)

8. Summary and discussion
Mass loading effect of the escaping O+ from the polar region is quantitatively substantial in decelerating the solar winds flow in the exterior cusp & plasma mantle.
The excess energy by this mass-loading effect is most likely converted to the electrostratic energy that powers a local dynamo (independent to global dynamo) that drives the cusp current system and related ionospheric convection. Agreement is quantitative.
The magnetosheath inflow experiences information that "the field is connected to the ionosphere" twice: first simple magnetic connectivity, and then by meeting the ionospheric outflowing ions for extra local deceleration. In this sense the cusp is "double open".
Resultant current system should be independent to Region 1 field aligned current (Figure 4).

9. OK OK