xmpl2d43.dat, x-ray tube with thermal energies.
The simulation is of an x-ray tube that has a flat thermionic cathode and target (anode) voltage 100kV.
No attempt has been made to optimise the instrument by varying the shapes and positions of the electrodes. In fact the beam spot size here is rather poor. There is severe spherical aberration. All the eletrodes have sharp edges. The numbers of segments and rays are small. The cathode has 20 segments and hence 20 rays start, but the suppression grid suppresses the outermost 5 rays.
The purpose of this example is only to illustrate some of the things that can be done to simulate an x-ray tube.
An important technical difficulty is that the potentials in the vicinity of the cathode need to be evaluated with an inaccuracy less than about 0.1eV, which is 1.E-6 of the anode voltage.
Another difficulty is that the beam has a length that is some orders of magnitude larger than the radius of the final spot at the target.
Here are some of the features of the present simulation:
(1) The potentials and fields in the region of the cathode are 'anchored' by an extra plate (described above as the 'cathode backing'). This extra plate has a relatively large number of segments.
(2) Only the parts of the electrodes that are 'seen' by the rays are included in the simulation. The outer parts are excluded and are replaced by 'bridges' that have linearly varying potentials.
(3) To reduce the computing time the requested fractional inaccuracies for the ray tracing and for the potentials and fields used during ray tracing are different. The second of these needs to be the lowest because the potentials and fields in the vicinity of the cathode need to be calculated very accurately. In fact the inaccuracy of the potentials must be less than 1.E-6 of the target voltage. On the other hand the first inaccuracy, used for the Bulirsch-Stoer technique of trajectory integration, can be higher to allow a faster computation. These two inaccuracies are specified above as 0.001 and 1E-06 (although for a final accurate run they would be reduced too 1E-4 and 1E-7).
(4) Again to reduce the computing time, the step lengths for the ray tracing are fairly long (but remember that the program subdivides each step into typically 16 parts to achieve the repuired accuracy). However the option is used to reduce the step length in the critical region near the cathode (see the line after the initial specification).
(5) The cathode is specified by giving the number of electrodes (in fact only 1 electrode, the first one) that constitute it (rather than giving the number of segments).
(6) One cathode ray starts from the centre of each cathode segment. If required, the cathode segments (which are ring-shaped) can all be given the same area by using an 'uneven' distribution that has the exponent p = -0.5.
(7) The random thermal velocity distribution of the cathode is dealt with by using the 'user-defined cathode' option of cpo2ds. This calls the external 'User-supplied' program cathode2.cpp, which is linked to the main program as cathode2.dll. The controlling data file cathode2.dat (called by cathode2.cpp) is:
100. maximum initial current density
1300. temperature, degrees K
1111 seed for random number generator
These data are also given in the present data file.
(8) To deal with the fact that the beam is long and thin, the 'space-charge tube' option is used. The option is used to reduce the radius of the tubes in the critical region near the cathode.
(9) In the present data file all the applied voltages are fixed and the rays are iterated only 2 times. To optimise the voltages (for example the 3rd and 4th voltages) the 'automatic focusing' option would be used. Here there would be 2 (or preferably more) ray iterations for each set of voltages. To do this the line:
n iterate to focus
could be substituted by:
ym iterate to focus
2 focus data, total number of different voltages to be varied
4 50 focus data, number of a voltage to be varied, and its excursion
3 50 focus data, number of a voltage to be varied, and its excursion
s 0 25 focus data, specified r and z of centre of focus
9 focus data, total number of rays to be considered
1e-06 20 focus data, tolerance level and maximum number of iterations
0.05 2 focus data, 'maximum distance' and 'penalty factor'
0 0 Number of voltage and angle limits
It must be emphasised again that the performance of the x-ray tube in the present simulation is poor. There is severe spherical aberration. As stated above, no attempt has been made to optimise the performance or the shapes and sizes of the electrodes. The purpose is only to illustrate the features that are needed in an accurate simulation.
(A confidential study for a commercial company, using comparable overall sizes and voltages, has achieved a final spot size that is significantly smaller. Interestingly, the radial intensity distribution in the spot has a double-peak structure caused by the spherical aberration introduced in the cathode region.)