CST – Computer Simulation Technology

C-Band On-Axis Coupled Standing Wave Linear Accelerator

Linear Accelerators (Linacs) are widely employed in accelerator facilities. Linear acceleration is the method of choice for light particles as synchrotron radiation effects limit the usability of circular accelerators for these particles. Industrial applications require compact linacs for the acceleration of electrons with target energy in the range between 1 and 25 MeV. CST MICROWAVE STUDIO® (CST MWS) and CST PARTICLE STUDIO® (CST PS) can be used to investigate the high frequency behaviour of linac structures as well as the interaction between particles and the accelerating field.

In figure 1, the design of an on-axis coupled standing wave linac structure is depicted. The structure is derived from an E010 pillbox resonator. It contains rotational symmetric main cells, in which the electrons actually gain energy, and short coupling cells for RF field distribution. The length of one main-cell-coupling-cell-lattice equals the distance which a relativistically moving electron (velocity v) covers during one half of the RF wave (t=1/(2f)). This ensures that the RF field within the main cells reverses polarity synchronously with particle movement....

Figure 1: Cut-away view of on-axis coupled 3-cell linac structure comprising two main and one coupling cell. The coupling slots of the right cell are tilted by 90° to prevent direct RF feedthrough.

From a microwave point of view, the structure in Fig. 1 behaves like a system of coupled cavity resonators. In the case of N+1 coupled resonators, the resonance frequency of the individual resonator splits into N+1 frequencies which vary in phase advance Δφ of the respective field patterns between adjacent resonators: Δφ = nπ / N where n = 0 … N. The Eigenmode solver of CST MWS can be used to calculate the three individual eigenfrequencies of the structure as a function of the phase advance between two adjacent cells. Figure 2 depicts the resulting Brillouin diagram together with data gathered by means of RF measurement. Very good agreement between the numerical and experimental approach was observed [1].

Figure 2: Simulation (blue) and measurement data concerning on-axis coupled 3-cell linac structure. The p/2-mode is spectrally located at 5.712 GHz as high power C-band RF sources necessary for exciting the accelerating field are available at this frequency.

Within the main cells, noses have been introduced to concentrate the longitudinal component of the electrical field on the beam propagation axis. The electric field amplitude directly at the noses is slightly higher than in the middle of the cell to make up for the time-varying sinusoidal increase and decrease of the field during the particle’s passage of the cavity. The electric field distribution within the 3-cell-model of figure 1 was simulatively captured using field monitors. Moreover, it was measured by means of the dielectric disturbation technique [3]. Figure 3 depicts the results of both approaches.

Figure 3: E-Field distribution within on-axis coupled 3-cell linac structure

To investigate the resonator-particle-interaction, the aforementioned model comprising three cells was expanded to a seven-cell-structure containing four main and three coupling cells. The 3rd out of 7 eigenmodes of this structure is the π / 2 – mode of the E010 field pattern which shows a phase advance between two adjacent cells of 90 degrees. In this mode, field nodes occur in the side cells and the field maxima are located in the main cells. Thus, when propagating down the structure, the synchronous particle “sees” only accelerating field as the field polarity is switched when the electron passes the coupling cavity.

Figure 4: p/2-mode of E010 field pattern

To include an electron beam in the calculation domain, the output of a thermionic gun was modelled by defining a small PEC-cylinder as emission surface on the beam propagation axis. The electron input energy was set to 60 keV and the DC beam emission current to 50 mA, respectively. The electric and magnetic field which were calculated beforehand were included as external field sources within the PIC solver. Due to a field gradient in the range of 20 MeV/m, the beam reaches relativistic velocities already after passing one main cell. Consequently, there is not the stringent necessity of a focusing magnetic field to keep the beam on track. Figure 5 depicts the output of a PIC position monitor which collected 180 shots of the particle distribution inside of the structure within a time span of 1.2 ns.

Figure 5: PIC position monitor output for electron movement in linac structure

Two main features of a standing-wave linac structure can be deducted from the simulation result in Fig. 5:

  1. The DC-injected electron beam is segmented into discrete electron bunches, as only a fraction of the injected particles are confronted with the correct RF phase. Furthermore, in the first cell a minor bunch expansion can be observed due to space charge forces at lower energies. Particles which are exposed to wrong phase within one of the middle cells can potentially reverse propagation direction and be accelerated towards the “gun”.
  2. Making their way through the accelerator, the correct-phase electrons gain energy cell by cell. In the example, the imported field leads to an energy gain of approximately 1.5 MeV / cell, causing a total output energy of 6.1 MeV. Moreover it can be observed that also lower-energy electrons reach the output section of the linac structure.

CST MWS and CST PS software packages can be used to effectively calculate both electromagnetic field distributions and cavity-particle-interaction inside of linear accelerator structures. In this article, design considerations regarding a C-Band linac structure have been described. Good agreement between CST simulation and measurement has been achieved on the microwave part of the structure.


[1] Design, simulation and measurement conducted by M. Ruf, K. Thurn and L.-P. Schmidt at Chair for High Frequency Technology, University of Erlangen-Nuremberg

[2] Toshiba Electron Tubes & Devices Co.,Ltd. (http://www.toshiba-tetd.co.jp/eng/electron/e_kly.htm, recalled March 9, 2011)

[3] L.C. Maier, J.C. Slater, "Field Strength Measurements in Resonant Cavities", Journal of Applied Physics, Volume 23 (1), Januar 1952

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