THE
COMPTON-GETTING
EFFECT
FOR
LOW
ENERGY
PARTICLES
SF.M.
Ipavich
University
of
Maryland,
College
Park,
Maryland
20742
Technical
Report
#74-117
H
June
1974-
H40
COLLEGE
PARK,
MARYLAND
Ict
0;4
U
11856-
U V S Y F A L
UNIVRSIT
OF
MARYLAND
DEATETOFPYISAN
SRNM
COLEE
AKMAYLN
THE
COMPTON-GETTING
EFFECT
FOR
LOW
ENERGY
PARTICLES
F.M.
Ipavich
University
of
Maryland,
College
Park,
Maryland
20742
Technical
Report
#74-117
June
1974
Space Physics
Group
THE
COMPTON-GETTING
EFFECT
FOR
LOW
ENERGY
PARTICLES
F.
M.
Ipavich
University
of
Maryland
College
Park,
Maryland
20742
ABSTRACT
The
traditional
first-order
Compton-Getting
effect,
which
relates
particle
distributions
as
observed
in
two
frames
of
reference
moving
with
constant
relative
velocity,
is
inadequate
for
the
description
of
low
energy
particles
(less
than
a
few
hundred
keV/nucleon)
in
the
solar
system.
An
exact
procedure
is
given for
recovering
both
isotropic
and
anisotropic
distributions
in
the
solar
wind
frame
from
observations
made
in a
spacecraft
frame.
The
method
is
illustrated
by
analyzing
a
particle
event
observed
by
the
University
of
Maryland
experiment
on
IMP-7
on
31
October
1972.
2
INTRODUCTION
A
distribution
of
particles
which
is
isotropic
in
one
frame
of
reference
will
display
an
anisotropy
if
observed
from
a
different
frame
of
reference.
This
is
referred
to
as
the
Compton-Getting
effect
(Compton
and
Getting,
1935).
For
nonrelativistic
particles
the
magni-
tude
of
the
induced
anisotropy
(Gleeson
and
Axford,
1968;
Forman,
1970)
is
equal
to
(2
+
2y)
(w/v),
where
y
is
the
spectral
index
of
the
parti-
cle
differential
intensity,
w
is
the
relative
speed
of
the
two
frames
of
reference,
and
v
is
the
particle
speed.
The
above
formula
assumes
w
<<
v.
Recently
Balogh,
et
al.
(1973)
have
derived
an
expression
for
the
anisotropy
accurate
to
order
(w/v)
2
.
For
particle
convection
induced
by
the
solar
wind,
w
is
equal
to
the
solar
wind
speed.
Present
day
satellite
experiments
respond
to
such
low
energies
that
the
assumption
w
<<
v
can
no
longer
be
used.
For
example,
one
detector
on
the
Univer-
sity
of
Maryland
experiment
on
IMP-8
responds
to
heavy
ions
with
energies
%20
keV/nucleon
(Tums,
et
al.,
1974).
Since
v
(km/sec)
=
440
[E(keV/
nucleon)]
2,
this
implies
v =
5 w
for
typical
solar
wind
speeds,
and
v
= 3
w
during
disturbed
periods.
Future
experiments
will
undoubtedly
reach
even
lower
energies.
In
this
letter
we
first
derive
an
exact
transformation
of
a
particle
distribution
which
is
isotropic
in
the
solar
wind
frame.
We
then
show
how
a distribution
with
arbitrarily
high
anisotropy
in
the
solar
wind
frame
may
be
transformed
exactly
into
the
observer's
frame.
The
procedure
is
illustrated
by
analyzing
one
of
the
"post-shock"
particle
spikes
dis-
cussed
by
Gloeckler,
et
al
(1974).
EXACT
TRANSFORMATION
FOR
ISOTROPIC
DISTRIBUTION
The
exact
transformation
procedure
is
based
on
the
Lorentz
invari-
ance
of
the
particle
distribution
function
in
phase
space
(Forman,
1970).
Let
primed
quantities
refer
to
t.en
solar
wind
frnme
and
unprimed
quan-
tities
to
the
observer's
frame.
All.
particles
are
assumed
to
be
non-
relativistic,
since
for
relativistic
particles
the
fiirst-order
Compton-
Getting
correction
is
a
perfectly
good
opproximation.
The
particle
momenta
in
the
two
frames
of
reference
are
related
by
the
Lorentz
transformation
P'
=
P- P
w/v()
Here
w
is
the
solar
wind
velocit1
and
v
is the
particle
speed.
(Equa-
tion
(1)
assumes
w
<<
speed
of
light).
The
magnitudes
of
the
momenta
are
related
by
P'
=
P
[1
-
2
(w/v)
cos
0 +
(w/vj)2]1/2,
(2)
where
0
is
the
angle
between
the
solar
wind
velocity
and
the
direction
in
which
the
observer
is
looking
(i.e.,
cos
0
=
(w-P)/(wP)).
The
distribution
function
f(P)
is
the
number
of
particles
of
momen-
tum
in
the
volume
element
dPx,
dPy,
dPz,
dx,
dy,
dz
of
phase
space.
As
demonstrated
by
Forman
(1970),
this
function
is
a
Lorentz
invariant:
f(P)
=
f'(P')
(3)