Upper Ionosphere of Mars During Solar Quiet and Disturbed Conditions - Planetary Exploration and Science: Recent Results and Advances - page 138

where g is the acceleration due to gravity and sj is the momentum transfer collision
frequency between species s and j . The charge on species s is equal to ˙ e depending
on whether s denotes electrons or ions; m s is the mass of charged particles; E and B
are the electric and magnetic fields, respectively; p s is the pressure ( D n s k B T s where
k B and T s are Boltzmann constant and temperature, respectively); and u n is the speed
of the neutral particle. The temperature for species s can be calculated by the energy
equation

K s

3
2 k B n s

@T s
@t

@
@ z

@T s
@ z

D Q s L s

(7.3)

where Q s and L s are heating and cooling rates, respectively, and K s is coefficient
of thermal conductivity. This energy equation leaves out dynamical terms such as
heat advection, which is less important for electrons than heat conduction and local
heating and cooling. Chen et al. ( 1978 ) and Rohrbaugh et al. ( 1979 )havesolved
energy equations to study ion and electron temperatures in the dayside ionosphere
of Mars. In the magnetised plasma, the momentum equation includes the magnetic
field (cf., Eq. 7.2 ), which can be derived from the so-called magnetic induction
equation. The induction equation can be written as

o rB

@ @t Dr . u s B / r

(7.4)

This equation is obtained by combining Faraday's law, the generalised Ohm's law
and Ampere's law and is known as the magnetic convection-diffusion equation. The
first term on the right-hand side of Eq. 7.4 is magnetic convection term, and the
second term is the magnetic diffusion term.
Apart from continuity, energy and momentum equations, there are MHD and
hybrid models, which are self-consistent Mars-solar wind plasma approaches
(cf. Nagy et al. 2004 ;Maetal. 2008 ; Kallio et al. 2010 ). MHD model provides
a high-resolution, three-dimensional simulation of the Martian ionosphere, which
contains both a solar wind and a self-consistent ionosphere. In this model, all ions
are assumed to have the same bulk velocity. Furthermore, it assumes a Maxwellian
velocity distribution function, while pickup ions O C are highly non-Maxwellian
on Mars. The hybrid model is also a three-dimensional model and has been used
to study the global modelling of the Mars-solar wind interaction (Modolo et al.
2006 ; Brecht and Ledvina 2006 ; Ledvina et al. 2008 ; Brain et al. 2010 ; Kallio et al.
2010 ). This model represents electrons as a massless fluid. The advantage of this
model is that it includes kinetic effects such as finite gyro radius of ions, wave
particle interaction and instabilities associated with the non-Maxwellian velocity
distribution function. Hybrid model has a low resolution. It does not include Martian
crustal magnetic anomalies because the limited resolution makes it impossible to
include a realistic crustal magnetic field model.