Abstract
We develop and test a numerical
code that provides a
self-consistent deconvolution of
energy-dependent hard X-ray (HXR)
time profiles I( varepsilon , t)
into two HXR-producing
electron components, i.e., directly
precipitating and
trap-precipitating electrons. These
two HXR
components can be physically
distinguished because their
energy-dependent time delays have
an
opposite sign. The deconvolution is
based on the following model
assumptions: (1) nonthermal
electrons are injected from the
acceleration site into coronal
flare loops by an injection
function f(E,
alpha , t) that consists of
synchronized pulses in energy E and
pitch angle alpha , (2) electrons
with initially small pitch angles (
alpha <= alpha 0) precipitate
directly to the HXR emission site,
(3) electrons with initially large
pitch angles ( alpha >= alpha 0)
are temporarily trapped and
precipitate after the collisional
deflection time, and (4) nonthermal
electrons lose their energy by
Coulomb collisions and emit
thick-target HXR bremsstrahlung in
a high-density (fully collisional)
site (near or inside the
chromosphere). The numerical
deconvolution provides a
self-consistent
determination of three physical
parameters: (1) the electron
time-of-flight distance lTOF
between the acceleration/injection
site and the HXR emission site, (2)
the electron density ne in
the trap region, and (3) the
fraction of HXR-emitting electrons
that precipitate directly, qprec,
which relates to the loss cone
angle by qprec( alpha 0) = (1 - cos
alpha 0) for isotropic pitch angle
distributions. This yields the
magnetic mirror ratio R =
Bloss/Binj = 1/sin2 ( alpha 0)
between the
injection and loss cone site. With
this method, we measure for the
first time magnetic field ratios
in coronal loops by means of HXR
data. Based on this ratio, together
with the knowledge of the
photospheric field at the
footpoint, a direct measurement of
the magnetic field in the coronal
acceleration region can be
obtained. We simulate
energy-dependent HXR data I(
varepsilon , t)
with typical solar flare parameters
(lTOF = 15,000 km, ne = 1011 cm-3,
qprec = 0.5) and test the
accuracy of the inversion code. We
perform the inversion in 30
different simulations over the
entire
physically plausible parameter
space and demonstrate that a
satisfactory inversion of all three
physical parameters lTOF, ne, and
qprec is achieved in a density
range of ne = 1010-1012 cm-3
for precipitation ratios of qprec =
0.1-0.9 and for signal-to-noise
ratios of >~100 (requiring HXR
count rates of >~104 counts s-1).
Applications of this inversion
method to solar flare
observations in hard X-rays
(CGRO/BATSE, Yohkoh/Hard X-Ray
Telescope) and
microwaves (Nobeyama)
will be presented in
subsequent papers.