- Email: [email protected]
Residence time heating effect in auroral conic generation
Planet. Space Sci., Vol. 32, No. 9, pp. 1115-I 117. 1984 Printed in Great Bntain.
RESIDENCE
0032-0633/8453.00 + 0.00 Q 1984 Pergamon Press Ltd.
TIME HEATING EFFECT CONIC GENERATION
IN AURORAL
J. L. HORWITZ
Department
of Physics, The University of Alabama in Huntsville, (Received 7 February
Huntsville,
AL 35899, U.S.A.
1984)
Abstract--It is pointed out that, in addition to previously considered microscopic aspects ofion perpendicular heating in the aurora1 region, the effect of mass-dependent resident times in a finite-length perpendicular heating region may be important. In a simple illustrative model, particles are assumed to enter upward into an aurora1 acceleration region of finite extent along B, in which both parallel electric fields and perpendicular heatingexist. In this situation, the particle residence times vary with particle mass as ML/‘, so that, in addition to effects associated with species-dependent heating rates, the resultant perpendicular energization associated with residence time also varies as Ml”. The residence time effect thus favors heating of heavier particles, and may therefore be of some importance in understanding the greater energization of oxygen over hydrogen that has been observed, and also why no electron tonics have been observed. 1.
INTRODUCTION
One of the most interesting recent discoveries in aurora1 phenomena is the tonics which have been observed in and above the aurora1 ionosphere (Sharp et al., 1977; Klumpar, 1979; Whalen et al., 1978; Gorney et nl., 1981; Horwitz, 1980; Horwitz et al., 1982). The perpendicular energization for the tonics is considered by most workers to result from interaction of ions with electrostatic waves of the ion cyclotron or lower hybrid types (e.g., Lysak et al., 1980; Papadopoulos et al., 1980; Singh et al., 1984). The effect of spatially varying convection electric fields in producing tonics has also been investigated (e.g., Lennartson, 1980). Collin et al. (1981) have observed that oxygen ions tend to be more energetic than hydrogen, typically by a factor of - 1.7. Models of the proposed ion heating have sought to explain this apparent mass dependence as resulting from differences in saturation heating levels (e.g., Papadopoulos et al., 1980; Singh et al., 1984). These authors found that heating tends to produce a maximum ion energization which varies as M513. Another interesting aspect of tonics is that such distributions have not yet been observed in electrons. As far as we are aware, the possible reasons for this absence of electron tonics have not been discussed. The purpose of this note is to point out that massdependent particle residence times may be of importance in the above aspects of aurora1 conic generation, in addition to species-dependent heating rates.
2. MODEL
For the present purposes, we will envisage an aurora1 acceleration layer in which a parallel electric field E,,
and a process causing perpendicular heating of particles are present for a finite distance L along the magnetic field direction. The parallel electric field is probably not essential to the point about residence times in the layer, since many processes would tend to cause slower flows of heavier particles ; however, the E ,, facilitates the illustration and is included here. We will neglect variation of the magnetic field within this distance L. Specifying the upgoing particle distribution at the base ofthe acceleration region, we will obtain the distribution exiting at the top to illustrate the dependence on mass of the particles associated with residence times for the resultant energization. The specification of the initial distribution at the bottom of the acceleration region will not be critical in determining the exiting distribution if the parallel and perpendicular acceleration dominate the initial characteristic energies of the upgoing particles ; here we will use the form of a streaming distribution :
w,,, ulr s = 0) = No&~-qo)
&v,).
(1)
Since the variation of the magnetic field is neglected here, there is no coupling between the parallel and perpendicular velocity components. The parallel velocityofthedistribution at the top(s = Qisrelated to its initial velocity as
where V is the total dotential drop across the layer, E ,,L. For the perpendicular energization, weallow the ions to be heated such that the ion temperature increases at a rate p, which may be species dependent, during the time the particles are within the layer. This would result, for example, from stochastic acceleration of ions at the
1115
1116
J. L. HORWITZ
fundamental ion gyrofrequency (e.g., Schmitt, 1976). The time in the layer is the same for all of the particles for the given choice of distribution function (1) and is
t layer=
L ds
2L
s 0 u(s)
(2qV/M)‘:2
-=
x [(l
+$!)?(!$~‘z].
(3)
If the initial streaming energy is much smaller than the energy from the electric potential of the layer (i.e., Mui J2q V cc l), then 2L
t layer=m.
(4)
c-1M The perpendicular distribution is then
temperature
at s = L for this
TL = ?-tlayer = 7-[2L/(2qV/M)“2]. at s = L then becomes
The exiting distribution
fy2 +
F(L~,,,VL’S= L) = N,
(5)
-[y2)
M
x(&)exp[ -(Ey-t6) The characteristic shape ofthe distribution will depend on the ratio of the average perpendicular energy (kT,) to the parallel energy (qV). The pitch angle of the characteristic particle is
[I -El
cc,=tan-’
= tan-’
{?!!$g+lI4].
(7)
We can say roughly that if CL~, > 45” the distribution is “pancake-like” and in the diverging magnetic field above the layer will form a conic, whereas the aL < 45” implies essentially a beam-like character for the emerging distribution. For two groups of particles of different masses M, and M,, same charge q, transversing the same layer, the ratio of the average perpendicular energies at the top of the layer is ~1@42)
EI(MI) where we have included different species.
As can be seen from equation (8), apart from massdependent heating rates, the perpendicular energization owing to the time-of-traversal effect illustrated here varies as M ‘I’. Hence, oxygen ions traversing such a layer will be energized four times as much as hydrogen ions in association with the residence time effect alone, if the perpendicular heating dominates the parallel energization. In this case, the parallel electric field’s importance is not so much in its contribution to particle energization as in its control of the time of traversal of the accelerating layer. In fact, had we assumed that the parallel electric field was confined to a layer just below the layer of perpendicular heating, instead of being mixed together, the same mass dependence would result, the only difference being that 21, + L in equations (3))(5) and (7). This framework may also provide insight into why there have not been observations ofelectron tonics. For illustration, suppose that for a given layer, the parallel electric-field and perpendicular heating rate are such that the characteristic pitch angle [equation (7)] for emerging oxygen ions is 70”, so that the emerging distribution can be said to be “pancake-shaped”. Considering, for purposes of illustration of the effects of the residence time alone, the same values for parallel electric field (sign reversed) and perpendicular heating rate for a layer which electrons now traverse, the pitch angle for the average emerging electron is tan CI, = tan(O+)(m,/Mo+)1’4 and with clo+ = 70” we have c(, = 11.8”.
l/2
&II
[
3. DISCUSSION
(8) different heating rates (0 for
Thus, the electrons emerge with more of a beam-like distribution. This model thus illustrates at least one effect which would discriminate against electrons forming conic distributions. The purpose of this note has been to focus on the mass-dependence of energization associated with timeof-residence in a limited acceleration region where both parallel electric fields and perpendicular heating are present. Obviously, the questions regarding specific processes causing the heating and the intrinsic massdependent aspects, whether the heating is an overall heating of the distribution or yields a suprathermal tail to the distribution, what the source of the parallel electric fields and perpendicular energization are, etc., have not been addressed as in a comprehensive model. Also, if the energization is saturated while in the layer, as in some of the previous models, rather than increasing with particle residence time as in the present model, then the mass-dependent effect shown here will
Residence not
be
a controlling
factor. the
question,
however,
dependent
energization
combination
of
a
pendicular
energization here, should
from
this
time-of-residence effect,
parallel
described
Apart
time heating
associated
electric
in a finite layer be of relevance
field which
effect in aurora1 conic generation last
masswith and
the per-
has been
to aurora1
conic
generation.
Acknowledgement-This Contract NAS8-33982 Huntsville.
research was supported by NASA at The University of Alabama in
4. REFERENCES Collin, H. L., Sharp, R. D., Shelley, E. G. and Johnson, R. G. (1981) Some general characteristics of upflowing ion beams over the aurora1 zone and their relationship to aurora1 electrons. J. geophys. Res. 86, 8820. Gorney, D. J., Clarke, A., Croley, D. R., Fennell, J. F., Luhmann, J. M. and Mizera, P. F. (1981) The distribution of ion beams and tonics below 8000 km. J. geophys. Res. 86,83. Horwitz, J. L. (1980) Conical distributions of low-energy ion fluxes at synchronous orbit. J. geophys. Res. 852057. Horwitz, J. L., Baugher, C. R., Chappell, C. R., Shelley, E. G. and Young, D. T. (1982) Conical pitch angle distributions of
1117
very low-energy ion fluxes observed by ISEE-1. J. geophys. Res. 81, 2311. Klumpar, D. M. (1979) Transversely accelerated ions: An ionospheric source of hot magnetospheric ions. J. geophys. Res. 84,4229. Lennartsson, W.(1980)0n theconsequencesoftheinteraction between the aurora1 plasma and the geomagnetic field. Planet. Space Sci. 28, 135. Lysak, R. L., Hudson, M. K. and Temerin, M. (1980) Ion heating by strong electrostatic ion cyclotron turbulence. J. geophys. Res. 85,678. Papadapoulos, K., Gaffey, J. B. Jr. and Palmadesso, P. J. (1980) Stochastic acceleration of large M/Q ions by hydrogen cyclotron waves in the magnetosphere. Geophys. Res. Lett. 7, 1014. Schmitt, J. P. M. (1976) Nonlinear theory of rf heating at cyclotron harmonics. Phys. Fluids 19,245. Sharp, R. D., Johnson, R. G. and Shelley, E. G. (1977) Observations of an ionospheric acceleration mechanism producing energetic (keV) ions primarily normal to the geomagnetic field direction. J. geophys. Res. 82, 3324. Singh, N., Schunk, R. W. and Sojka, J. J. (1984) Preferential perpendicular acceleration of heavy ionospheric ions by interactions withelectrostatic hydrogen cyclotron waves. J. .qeophys. Res. (in press). Whalen, B., Bernstein, A. W. and Daly, P. W. (1978) Lowaltitudeacceleration ofionospheric ions. Geophys. Rex Lett. 5, 55.
RESIDENCE
0032-0633/8453.00 + 0.00 Q 1984 Pergamon Press Ltd.
TIME HEATING EFFECT CONIC GENERATION
IN AURORAL
J. L. HORWITZ
Department
of Physics, The University of Alabama in Huntsville, (Received 7 February
Huntsville,
AL 35899, U.S.A.
1984)
Abstract--It is pointed out that, in addition to previously considered microscopic aspects ofion perpendicular heating in the aurora1 region, the effect of mass-dependent resident times in a finite-length perpendicular heating region may be important. In a simple illustrative model, particles are assumed to enter upward into an aurora1 acceleration region of finite extent along B, in which both parallel electric fields and perpendicular heatingexist. In this situation, the particle residence times vary with particle mass as ML/‘, so that, in addition to effects associated with species-dependent heating rates, the resultant perpendicular energization associated with residence time also varies as Ml”. The residence time effect thus favors heating of heavier particles, and may therefore be of some importance in understanding the greater energization of oxygen over hydrogen that has been observed, and also why no electron tonics have been observed. 1.
INTRODUCTION
One of the most interesting recent discoveries in aurora1 phenomena is the tonics which have been observed in and above the aurora1 ionosphere (Sharp et al., 1977; Klumpar, 1979; Whalen et al., 1978; Gorney et nl., 1981; Horwitz, 1980; Horwitz et al., 1982). The perpendicular energization for the tonics is considered by most workers to result from interaction of ions with electrostatic waves of the ion cyclotron or lower hybrid types (e.g., Lysak et al., 1980; Papadopoulos et al., 1980; Singh et al., 1984). The effect of spatially varying convection electric fields in producing tonics has also been investigated (e.g., Lennartson, 1980). Collin et al. (1981) have observed that oxygen ions tend to be more energetic than hydrogen, typically by a factor of - 1.7. Models of the proposed ion heating have sought to explain this apparent mass dependence as resulting from differences in saturation heating levels (e.g., Papadopoulos et al., 1980; Singh et al., 1984). These authors found that heating tends to produce a maximum ion energization which varies as M513. Another interesting aspect of tonics is that such distributions have not yet been observed in electrons. As far as we are aware, the possible reasons for this absence of electron tonics have not been discussed. The purpose of this note is to point out that massdependent particle residence times may be of importance in the above aspects of aurora1 conic generation, in addition to species-dependent heating rates.
2. MODEL
For the present purposes, we will envisage an aurora1 acceleration layer in which a parallel electric field E,,
and a process causing perpendicular heating of particles are present for a finite distance L along the magnetic field direction. The parallel electric field is probably not essential to the point about residence times in the layer, since many processes would tend to cause slower flows of heavier particles ; however, the E ,, facilitates the illustration and is included here. We will neglect variation of the magnetic field within this distance L. Specifying the upgoing particle distribution at the base ofthe acceleration region, we will obtain the distribution exiting at the top to illustrate the dependence on mass of the particles associated with residence times for the resultant energization. The specification of the initial distribution at the bottom of the acceleration region will not be critical in determining the exiting distribution if the parallel and perpendicular acceleration dominate the initial characteristic energies of the upgoing particles ; here we will use the form of a streaming distribution :
w,,, ulr s = 0) = No&~-qo)
&v,).
(1)
Since the variation of the magnetic field is neglected here, there is no coupling between the parallel and perpendicular velocity components. The parallel velocityofthedistribution at the top(s = Qisrelated to its initial velocity as
where V is the total dotential drop across the layer, E ,,L. For the perpendicular energization, weallow the ions to be heated such that the ion temperature increases at a rate p, which may be species dependent, during the time the particles are within the layer. This would result, for example, from stochastic acceleration of ions at the
1115
1116
J. L. HORWITZ
fundamental ion gyrofrequency (e.g., Schmitt, 1976). The time in the layer is the same for all of the particles for the given choice of distribution function (1) and is
t layer=
L ds
2L
s 0 u(s)
(2qV/M)‘:2
-=
x [(l
+$!)?(!$~‘z].
(3)
If the initial streaming energy is much smaller than the energy from the electric potential of the layer (i.e., Mui J2q V cc l), then 2L
t layer=m.
(4)
c-1M The perpendicular distribution is then
temperature
at s = L for this
TL = ?-tlayer = 7-[2L/(2qV/M)“2]. at s = L then becomes
The exiting distribution
fy2 +
F(L~,,,VL’S= L) = N,
(5)
-[y2)
M
x(&)exp[ -(Ey-t6) The characteristic shape ofthe distribution will depend on the ratio of the average perpendicular energy (kT,) to the parallel energy (qV). The pitch angle of the characteristic particle is
[I -El
cc,=tan-’
= tan-’
{?!!$g+lI4].
(7)
We can say roughly that if CL~, > 45” the distribution is “pancake-like” and in the diverging magnetic field above the layer will form a conic, whereas the aL < 45” implies essentially a beam-like character for the emerging distribution. For two groups of particles of different masses M, and M,, same charge q, transversing the same layer, the ratio of the average perpendicular energies at the top of the layer is ~1@42)
EI(MI) where we have included different species.
As can be seen from equation (8), apart from massdependent heating rates, the perpendicular energization owing to the time-of-traversal effect illustrated here varies as M ‘I’. Hence, oxygen ions traversing such a layer will be energized four times as much as hydrogen ions in association with the residence time effect alone, if the perpendicular heating dominates the parallel energization. In this case, the parallel electric field’s importance is not so much in its contribution to particle energization as in its control of the time of traversal of the accelerating layer. In fact, had we assumed that the parallel electric field was confined to a layer just below the layer of perpendicular heating, instead of being mixed together, the same mass dependence would result, the only difference being that 21, + L in equations (3))(5) and (7). This framework may also provide insight into why there have not been observations ofelectron tonics. For illustration, suppose that for a given layer, the parallel electric-field and perpendicular heating rate are such that the characteristic pitch angle [equation (7)] for emerging oxygen ions is 70”, so that the emerging distribution can be said to be “pancake-shaped”. Considering, for purposes of illustration of the effects of the residence time alone, the same values for parallel electric field (sign reversed) and perpendicular heating rate for a layer which electrons now traverse, the pitch angle for the average emerging electron is tan CI, = tan(O+)(m,/Mo+)1’4 and with clo+ = 70” we have c(, = 11.8”.
l/2
&II
[
3. DISCUSSION
(8) different heating rates (0 for
Thus, the electrons emerge with more of a beam-like distribution. This model thus illustrates at least one effect which would discriminate against electrons forming conic distributions. The purpose of this note has been to focus on the mass-dependence of energization associated with timeof-residence in a limited acceleration region where both parallel electric fields and perpendicular heating are present. Obviously, the questions regarding specific processes causing the heating and the intrinsic massdependent aspects, whether the heating is an overall heating of the distribution or yields a suprathermal tail to the distribution, what the source of the parallel electric fields and perpendicular energization are, etc., have not been addressed as in a comprehensive model. Also, if the energization is saturated while in the layer, as in some of the previous models, rather than increasing with particle residence time as in the present model, then the mass-dependent effect shown here will
Residence not
be
a controlling
factor. the
question,
however,
dependent
energization
combination
of
a
pendicular
energization here, should
from
this
time-of-residence effect,
parallel
described
Apart
time heating
associated
electric
in a finite layer be of relevance
field which
effect in aurora1 conic generation last
masswith and
the per-
has been
to aurora1
conic
generation.
Acknowledgement-This Contract NAS8-33982 Huntsville.
research was supported by NASA at The University of Alabama in
4. REFERENCES Collin, H. L., Sharp, R. D., Shelley, E. G. and Johnson, R. G. (1981) Some general characteristics of upflowing ion beams over the aurora1 zone and their relationship to aurora1 electrons. J. geophys. Res. 86, 8820. Gorney, D. J., Clarke, A., Croley, D. R., Fennell, J. F., Luhmann, J. M. and Mizera, P. F. (1981) The distribution of ion beams and tonics below 8000 km. J. geophys. Res. 86,83. Horwitz, J. L. (1980) Conical distributions of low-energy ion fluxes at synchronous orbit. J. geophys. Res. 852057. Horwitz, J. L., Baugher, C. R., Chappell, C. R., Shelley, E. G. and Young, D. T. (1982) Conical pitch angle distributions of
1117
very low-energy ion fluxes observed by ISEE-1. J. geophys. Res. 81, 2311. Klumpar, D. M. (1979) Transversely accelerated ions: An ionospheric source of hot magnetospheric ions. J. geophys. Res. 84,4229. Lennartsson, W.(1980)0n theconsequencesoftheinteraction between the aurora1 plasma and the geomagnetic field. Planet. Space Sci. 28, 135. Lysak, R. L., Hudson, M. K. and Temerin, M. (1980) Ion heating by strong electrostatic ion cyclotron turbulence. J. geophys. Res. 85,678. Papadapoulos, K., Gaffey, J. B. Jr. and Palmadesso, P. J. (1980) Stochastic acceleration of large M/Q ions by hydrogen cyclotron waves in the magnetosphere. Geophys. Res. Lett. 7, 1014. Schmitt, J. P. M. (1976) Nonlinear theory of rf heating at cyclotron harmonics. Phys. Fluids 19,245. Sharp, R. D., Johnson, R. G. and Shelley, E. G. (1977) Observations of an ionospheric acceleration mechanism producing energetic (keV) ions primarily normal to the geomagnetic field direction. J. geophys. Res. 82, 3324. Singh, N., Schunk, R. W. and Sojka, J. J. (1984) Preferential perpendicular acceleration of heavy ionospheric ions by interactions withelectrostatic hydrogen cyclotron waves. J. .qeophys. Res. (in press). Whalen, B., Bernstein, A. W. and Daly, P. W. (1978) Lowaltitudeacceleration ofionospheric ions. Geophys. Rex Lett. 5, 55.