The ion temperature gradient: An intrinsic property of Earth’s magnetotail

by San Lu


Spacecraft observations have revealed that ion temperature in the Earth's magnetotail is nonuniform in both the Earth-tail (in the GSM x direction, along the magnetotail) and north-south (in the GSM z direction, across the magnetotail) directions. The ion temperature has been found to increase in the earthward direction, i.e., higher in the near-Earth regions. The earthward ion temperature gradient balances magnetic tension forces caused by the magnetotail magnetic field configuration. The ion temperature gradient also exists in the north-south direction, which is shown by a bell-shaped ion temperature Ti profile versus Bx (Bx is a proxy of distance from the neutral sheet). To better understand the observed temperature profiles in the magnetotail, a key question needs to be addressed: What is the relationship between the x gradient and the z gradient of ion temperature? Global hybrid simulation, being able to describe (1) ion convection motion in a global scale from the lunar distance to the near-Earth plasma sheet edge and (2) small-scale ion kinetics (important to resolve ion isotropization caused by scattering within the magnetotail current sheet), is used in this study to reveal the mechanism responsible for the temperature gradient.

Figure 1. Ion temperature Ti(keV) versus magnetic field |Bx |(nT), black and grey circles indicate measured data, and colored curves with errors show averaged data: THEMIS D at x≈-10RE (grey curve, filled black circles), Geotail at x≈-25RE (blue curve, empty black circles), and ARTEMIS P1 at x≈-55RE (red curve, filled grey circles). For each averaged profile, we show day (in brackets) and time interval of measurements.


THEMIS, Geotail, and ARTEMIS spacecraft simultaneously observe the magnetotail at different geocentric distances. Figure 1 shows three events of THEMIS D, Geotail, and ARTEMIS P1 conjunct observations of Ti (Bx ) at different distances from the Earth. THEMIS D crossed the current sheet at x≈-10RE; Geotail crossed the current sheet at x≈-25RE; and ARTEMIS P1 crossed the current sheet around lunar orbit x≈-55RE. The temperature profiles are similar in the three geocentric distances: higher at the current sheet center and decrease towards the current sheet upper and lower boundaries. The ion temperature is also higher in the near-Earth (observed by THEMIS D) and decreases towards the downtail. The multispacecraft observations show that the ion temperature gradient is a universal intrinsic property of the Earth’s magnetotail.

Figure 2. Global hybrid simulation (ANGIE3D) result of ion temperature distribution in the x-z plane of the magnetotail averaged over -10R_E≤y≤10R_E at a representative time, t=1430s.

A three-dimensional global hybrid simulation using ANGIE3D (AuburN Global hybrId codE in 3-D) is performed to investigate how the temperature gradient is formed. Figure 2 shows the simulation result, the ion temperature distribution in the x-z plane. The simulation well reproduces the observed ion temperature profile: higher at the current sheet center and decreases towards current sheet boundary (in the z direction) and downtail (in the x direction). By showing the absence of field-aligned gradient of ion temperature, we demonstrate that the mapping of the x gradient of ion temperature along magnetic field lines processes the bell-shaped Ti (Bx ) profiles.


Using simultaneous THEMIS D, Geotail, and ARTEMIS P1 observations, we show that the Ti (Bx ) profiles are ubiquitously bell-shaped in the magnetotail. We use 3-D global hybrid simulations to describe how the profiles are formed. According to the simulation results, in the absence of a field-aligned gradient of the ion temperature, the Ti (x) profile is mapped along magnetic field lines and forms the bell-shaped Ti (Bx ) profile in the z direction.


Lu, S., A. V. Artemyev, V. Angelopoulos, Y. Lin, and X. Y. Wang (2017), The ion temperature gradient: An intrinsic property of Earth’s magnetotail, J. Geophys. Res. Space Physics, 122, doi:10.1002/2017JA024209.

Biographical Note

San Lu is an Assistant Researcher in space physics at the University of California, Los Angeles. His primary research interests are computer simulations (particle-in-cell and hybrid) of space and laboratory plasma physics.

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