**Before we can calculate the hard ****x-ray**** emission from our loop
model, we must first specify how the accelerated ****electrons**** are
distributed in energy. That is, we need to specify what energies the electrons
have and how many electrons are at each energy. Experience with hard x-ray
****spectra**** from flares has shown that the number of electrons per unit energy
decreases with increasing energy. The number of 300 ****keV**** electrons is typically
many orders of magnitude (many factors of 10) smaller than the number of 30
keV electrons. **

**Flare hard x-ray spectra as well as the electron distributions responsible for
them are usually well described by a ****power law****. If ****E**** represents the electron
energy, the power law states that the number of electrons at energy ****E**** is
proportional to ****E**^{-p}**, where ****p****, the ****power-law index****, is a positive number. For ****p****
equal to 5, the value we adopt here, the ratio of the number of electrons at 30
keV to the number of electrons at 300 keV is (300 keV/30 keV)**^{5}**. Therefore, the
number of electrons at 30 keV is 100000 ( 10**^{5 }**) times greater than the number of
electrons at 300 keV. **

**Mathematically, our power law indicates that there is an infinite number of
electrons with zero energy. Since this cannot be true physically, there must be
some deviation from such a power law at low energies. For our model we
assume a sharp ****low-energy cutoff**** at 30 keV. That is, we assume that no electrons
are injected with energies below 30 keV. **

**We also need to specify the ****density**** of the injected electrons. We take the total
number density (summed over all electron energies) to be 2 x 10**^{8}** cm**^{-3}**. **

**For this electron distribution we can calculate that 1.6 x 10**^{35}** electrons are
injected into the cusp every second. The corresponding ****energy flux**** of injected
electrons is 1.1 x 10**^{28}** ****ergs**** s**^{-1}**. **

** Next: The Computed Images****
**