CST – Computer Simulation Technology

Dipole Magnet as Spectrometer for 5 MeV Electron Beams

AREAL (Advanced Research Electron Accelerator Laboratory) is the laser driven RF gun based electron linear accelerator project at CANDLE Synchrotron Research Institute in Armenia. The aim of the project is to produce small emittance ultra-short electron beam pulses for advanced experimental study in the fields of novel accelerator concepts, new coherent radiation sources and dynamics of atomic and molecular processes.

The presented dipole magnet is part of the magnetic spectrometer for 5MeV electron beam energy and energy spread measurements. The measurements are based on the dependence of the beam orbit in a magnetic field on the particles' energy.

Charged particles moving in a magnetic field will follow circular trajectories. The centripetal force for these trajectories results from the Lorentz Force ...

F = q v B, where q and v are the particle's charge and velocity and B is the magnetic field perpendicular to the velocity direction. Combining this with the formula for centripetal force, where m is the mass of the particle, gives equation (1), which can be rearranged to find the radius as a function of the magnetic field (2).

Figure 1: Radius of a particle trajectory in a magnetic field

If several charged particles with the same rest mass traverse a magnetic field, they can be differentiated in their velocity according to the radius of their trajectory: The larger the radius, the larger their velocity.

The magnetic field to bend the particles is realized by a dipole magnet, which is illustrated in figure 2. The yoke is made of a non-linear steel material, such that the B(H) curve of the material can be taken into account by the Magnetostatic solver of CST EM STUDIO® (CST EMS). The whole magnet is driven by 2 stranded coils, which are represented by built-in models in CST EMS. The coil current is 10A and 500 turns are considered. The particles are launched in the depicted direction.

Figure 2: Structure of the Dipole Magnet

The first result of interest in the design of such a magnet is certainly the magnetic field. This is shown in figure 3 in a cut view. On the left the H-field is shown, which occurs mainly in the air gap, while on the right the B field concentration in the iron yoke is illustrated.

Figure 3: H-field (left) and B-field (right) of the dipole magnet

For a detailed investigation according to [1] the fields along the particle trajectory also have to be evaluated. This can be done via post processing of the 3D fields along curves. As an example, the B-field along two curves is shown in figure 4.

Figure 4: B_y along the z-axis (upper diagram) and along the y-axis (lower diagram)

As final result the particle tracking solver of CST PARTICLE STUDIO® (CST PS) gives the trajectories of 5 particles, started at the same position but with different energies. The energy varies between 4 and 5 MeV in steps of 0.25MeV.

Figure 5: Particle trajectory for different energies

As expected from equation (2), the particle with the largest velocity (or energy) shows the largest radius. The whole analysis can be further improved by using particle monitors as screens and integrating the magnetic field along the particle's trajectory. Since this is beyond the scope of this article, please refer to [1]. The results of the simulation agree also quite well to measurements as can be found in [2].

[1] Andranik Tsakanian, "AREAL Dipole Magnet for 5MeV Electron Beam", CANDLE internal report, Yerevan, Armenia

[2] Andranik Tsakanian, "First Measurements of AREAL Dipole Magnet", AREAL project meeting, October 2013, Yerevan, Armenia / www.candle.am

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