ISSI Visiting Scientists Programme

__RHESSI SPECTRA:
__

__RECONSTRUCTION OF THE
DIFFERENTIAL EMISSION MEASURE__

Any interpretation of the mean electron flux spectrum f(E) requires model dependent assumptions. Under a purely thermal interpretation of the equation

(see Rhessi spectra: reconstruction of the electron spectrum), it can be shown [1] that the equation

occurs, where T is the temperature, k is the Boltzmann constant and the
differential emission measure ξ(T) is defined as:

with n(**r**) the plasma density and S_{T} a constant temperature
surface.

We observe that, in principle, the inversion of Equation (2) can be performed
using the same Tikhonov method described for the non-thermal problem. However,
the presence of the exponential function in the integral kernel increases
dramatically the numerical instability of the problem and reduces significantly
the effectiveness of any inversion approach.

Therefore, while, for the non-thermal problem, zero order (L=I) or first order
(L=D) regularizations are equally effective, in the thermal model zero-order
regularization does not assure a sufficient degree of smoothness and the choice
of first order regularization becomes essential.

**REFERENCES**

[1] Brown J. C. 1974 in G. A. Newkirk (ed.), Coronal Disturbances, *IAU Symp.
***57,** 395

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