On the design of wide-field x-ray telescopes
X-ray telescopes having a relatively wide field-of-view and spatial resolution vs. polar off-axis angle curves much flatter than the parabolic dependence characteristic of Wolter I designs are of great interest for surveys of the X-ray sky and potentially for study of the Sun's X-ray emission. We discuss the various considerations affecting the design of such telescopes, including the possible use of polynomial mirror surface prescriptions, a method of optimizing the polynomial coefficients, scaling laws for mirror segment length vs. intersection radius, the loss of on-axis spatial resolution, and the positioning of focal plane detectors.
Methods of optimizing x-ray optical prescriptions for wide-field applications
We are working on the development of a method for optimizing wide-field X-ray telescope mirror prescriptions, including polynomial coefficients, mirror shell relative displacements, and (assuming 4 focal plane detectors) detector placement along the optical axis and detector tilt. With our methods, we hope to reduce number of Monte-Carlo ray traces required to search the multi-dimensional design parameter space, and to lessen the complexity of finding the optimum design parameters in that space. Regarding higher order polynomial terms as small perturbations of an underlying Wolter I optic design, we begin by using the results of Monte-Carlo ray traces to devise trial analytic functions, for an individual Wolter I mirror shell, that can be used to represent the spatial resolution on an arbitrary focal surface. We then introduce a notation and tools for Monte-Carlo ray tracing of a polynomial mirror shell prescription which permits the polynomial coefficients to remain symbolic. In principle, given a set of parameters defining the underlying Wolter I optics, a single set of Monte-Carlo ray traces are then sufficient to determine the polymonial coefficients through the solution of a large set of linear equations in the symbolic coefficients. We describe the present status of this development effort.
General expression for the density effect for the ionization loss of charged particles
The equations for the density-effect correction $\ensuremath{\delta}(X)$ for the ionization loss as given in a previous paper have been extended to the case where $\ensuremath{\delta}({X}_{0})\ensuremath{\equiv}{\ensuremath{\delta}}_{0}g0$. Here ${X}_{0}$ is the lower limit of the range ${X}_{0}lXl{X}_{1}$, where a particularly simple expression for $\ensuremath{\delta}(X)$ applies; $X={log}_{10}(\frac{p}{{m}_{0}c})$, where $p$ is the momentum and ${m}_{0}$ is the mass of the incident particle. The case ${\ensuremath{\delta}}_{0}g0$ applies directly to the calculation of $\ensuremath{\delta}(X)$ for conductors (metals).