Accelerator Experience (Dr. S. Rakityansky)

Accelerator Experience

During 9 years (from 1981 to 1990) I worked as an accelerator engineer in a team constructing the Linear Induction Accelerator of electrons (LIU-30) in the Joint Institute for Nuclear Research (Dubna).

It was an innovative project since the accelerator was designed to produce electron beam with rather unusual parameters. The electron pulses were intended to generate secondary pulses of neutrons by bombarding a plutonium target kept under sub-critical conditions all the time. Therefore the beam had to carry at least 200A of average current and 30MeV of energy per particle.
Thus, it was very intensive beam and the main problem we faced was its huge space charge. Firstly, the beam tended to rapidly expand, and secondly to laterally shift from the axis as a result of attraction to its mirror image in the conducting walls of the accelerator tube. Coherent instabilities were also caused by inevitable deviations (though very small) of all elements of the accelerating track from axial symmetry.

Since our team was rather small (15 people), I was involved practically in all activities associated with design of the electron optics, its implementation, tests, and analysis of experimental data. Although my main duties were computer modeling and all sorts of calculations as well as theoretical analysis, many times I took part in physical installation of new equipment using wrench and screw-driver.

Dealing with an electron beam of very high intensity, we tried to keep the flow of electrons as close to laminar one as possible. To this end we designed a source of electrons (electron gun) with a special geometry and the optical system with minimal disturbance of the laminar flow. With beams of high intensity instabilities caused by its coherent oscillations significantly limit the length to which the beam can be transported through the optical system. I developed a new stochastic method for analyzing the tolerances within which this system may deviate from axial symmetry. Some of the results obtained and methods used are published in the papers 7, 9, 10, 12, and 13 listed in the Appendix A.

During my work in the accelerator team I solved the following problems:

Electron gun: I developed physical concept, mathematical model, and computer program (in FORTRAN) that automatically optimized geometry of the electrodes in order to obtain a laminar flow of electrons at the outlet of the electron gun. This involved iterative solution of the self-consistent problem of electron beam moving in the electric field formed by both the electrodes and the beam itself. The beam was divided in ~25 coaxial tubes of current or "macroparticles" which interacted with each other.
For a fixed distribution of the space charge given by the configuration of the macroparticle trajectories, the Poisson equation was solved to obtain the potential. In this potential, the relativistic equations describing motion of the macroparticles, were solved. This procedure repeated until the configuration of the trajectories stabilizes within a required accuracy. Then, if this configuration was turbulent, certain adjustment of the geometry was (automatically) done and everything started all over again.
In this way I designed a source of electrons with laminar flow that was much easier to transport through the accelerating channel.

Beam
transportation: The accelerating track (~200m) had 2 focusing solenoids at every 1.5m of its length (between the accelerating sections). It was impossible to empirically (by the try and error method) find a proper combination of magnitudes of the magnetic fields generated by all these solenoids, which would keep the beam from expanding. With very huge space charge, the beam required a gentle handling: If somewhere it was compressed too much, very soon it was out of control. To solve the problem, I developed physical concept, mathematical model, and computer program (in FORTRAN) that automatically optimized the magnetic fields keeping the beam radius from excessive oscillations. Similarly to the electron gun problem, the relativistic equations of macroparticle motion were solved self-consistently and the oscillations of the beam radius were minimized by minimizing the sum of squares of its deviations from an average value at a series of points as a function of the magnetic field magnitudes. This helped the operators to tune the focusing system.

Coherent
oscillations: Ideally, the accelerating track should be axially symmetric. In practice, however, this can never be achieved. Some elements are always shifted, inclined, and sagged. When analyzing the effect of these "defects" on the intensive beam, I found that maximal length to which the beam can be transported depends on the size of these defects. The beam as a whole, moves as a spiral around the geometric axis (coherent oscillations) with increasing amplitude and finally strikes the tube. Dealing with this problem, I developed physical concept, mathematical model, and computer program (in FORTRAN) that calculated maximal length to which the beam could be transported with given tolerances of the defects. Since actual displacements, and inclinations of individual elements were unknown, I fixed them randomly, assuming a Gaussian distribution within the tolerances. Repeating the calculations many times, I found the mean value of the maximal length and its standard deviation for given tolerances.

It should be emphasized that all computer programs that I used for these calculations were written by myself. At that time I did everything in FORTRAN which was not an object-oriented language. If I need to solve such problems today, I would prefere C++ or JAVA where a series of repeated accelearting and focusing structures can be programmed as repeated objects of the same type.

Links to the other pages of this CV:
=========================>>>

Electron gun:	I developed physical concept, mathematical model, and computer program (in FORTRAN) that automatically optimized geometry of the electrodes in order to obtain a laminar flow of electrons at the outlet of the electron gun. This involved iterative solution of the self-consistent problem of electron beam moving in the electric field formed by both the electrodes and the beam itself. The beam was divided in ~25 coaxial tubes of current or "macroparticles" which interacted with each other. For a fixed distribution of the space charge given by the configuration of the macroparticle trajectories, the Poisson equation was solved to obtain the potential. In this potential, the relativistic equations describing motion of the macroparticles, were solved. This procedure repeated until the configuration of the trajectories stabilizes within a required accuracy. Then, if this configuration was turbulent, certain adjustment of the geometry was (automatically) done and everything started all over again. In this way I designed a source of electrons with laminar flow that was much easier to transport through the accelerating channel.

Beam transportation:	The accelerating track (~200m) had 2 focusing solenoids at every 1.5m of its length (between the accelerating sections). It was impossible to empirically (by the try and error method) find a proper combination of magnitudes of the magnetic fields generated by all these solenoids, which would keep the beam from expanding. With very huge space charge, the beam required a gentle handling: If somewhere it was compressed too much, very soon it was out of control. To solve the problem, I developed physical concept, mathematical model, and computer program (in FORTRAN) that automatically optimized the magnetic fields keeping the beam radius from excessive oscillations. Similarly to the electron gun problem, the relativistic equations of macroparticle motion were solved self-consistently and the oscillations of the beam radius were minimized by minimizing the sum of squares of its deviations from an average value at a series of points as a function of the magnetic field magnitudes. This helped the operators to tune the focusing system.

Coherent oscillations:	Ideally, the accelerating track should be axially symmetric. In practice, however, this can never be achieved. Some elements are always shifted, inclined, and sagged. When analyzing the effect of these "defects" on the intensive beam, I found that maximal length to which the beam can be transported depends on the size of these defects. The beam as a whole, moves as a spiral around the geometric axis (coherent oscillations) with increasing amplitude and finally strikes the tube. Dealing with this problem, I developed physical concept, mathematical model, and computer program (in FORTRAN) that calculated maximal length to which the beam could be transported with given tolerances of the defects. Since actual displacements, and inclinations of individual elements were unknown, I fixed them randomly, assuming a Gaussian distribution within the tolerances. Repeating the calculations many times, I found the mean value of the maximal length and its standard deviation for given tolerances.