Design and Analysis of RF Section and Beam Wave Interaction for C Band 250 kW CW High Power Klystron

Klystron is vacuum electron device operating in microwave range of frequencies. It is used as power amplifier in a variety of systems including radars, particle accelerators and thermonuclear reactors. A precise simulation of beam wave interaction in klystron is useful not only to understand its operation but also in development of tube with minimum iterations in fabrication. In the present case standard design codes like POISSON'S SUPERFISH, AJDISK and MAGIC 2D have been used to estimate and optimize different design parameters of klystron for desired tube performance. The paper presents the results of RF-section simulation of 250 kW CW C-band klystron with specifications as given in Table 1.


Introduction
RF section has been désigned for interaction between electron beam from electron gun and modulating signal coming from input cavity of the klystron . The RF-section consists of two main parts:

Resonant Cavities
The input and the output are taken from the tube via the resonant cavities. The exchange of energy between accelerated electron beam and RF signal takes place at the gap of cavity.

Drift Tubes
The RF interaction structure essentially consists of a series of reentrant cavity resonators connected together with metallic pipes called drift tubes. Drift tube is the space between two successive cavities. In the drift length the electrons group into bunches after undergoing a change in velocity while passing through the cavity gap.
A 250 kW CW C-Band klystron with specifications as given in Table1 is under development at CEERI, Pilani (India). It is to be used as a RF source in ITER program.

Theory, Simulation, Results and Discussions
Poisson's Superfish is a collection of programs for calculating static magnetic and electric fields and radio-frequency electromagnetic fields in either 2-D Cartesian coordinates or axially symmetric cylindrical coordinates. The programs generate a triangular mesh fitted to the boundaries of different materials in the problem geometry. Plotting programs and other postprocessor codes present the results in various forms. The design of individual Cavities and calculation of their respective R/Q is done in Poisson's Superfish. RF cavity of 5GHz is designed by varying its radius to optimized resonant frequency and R/Q value of input and output cavities. Drift tube nose angle variation optimized to find correct value of cavity R/Q.     Fig. 1 to Fig. 4, it is understood that the frequency and R/Q values decrease as the tapering angle of the nose increases. It is also understood that the field amplitude at the center of the gap decreases with increasing tapering angle and is minimum for the round ended drift tube nose configuration and the fields bugle more and they are more divergent as the tapering angle decreases. However, the fields are smoother and less divergent in case of flat ended drift tube nose configurations.

Modeling Aspects of Re-entrant Cavity
The design aspects of cavities are being discussed here. The optimum design of the cavity follows the choice of the beam parameter such as beam current, voltage, perveance and diameter. The main parameters involve in the design cavity resonators are the gap length, drift tube radius, diameter and height of outer concentric cylinder, shunt impedance and quality factor of the cavity and finally the coupling.
Re-entrant type resonators cavity oscillates with wavelength λ/4, 3λ/4, 5λ/4 etc. so height of re-entrant cavity resonator is chosen to be slightly λ/4 for the frequency range. Here λ is free shape wave length. The gap length is chosen in such a way that the beam coupling coefficient is close to unity and transit angle across the gap is nearly 1 radian. It is very difficult to assess the Q and R/Q value of the cavity very accurately following conventional method. So we find these values from Computer Aided Simulation. The output coupling system is designed as per the requirements of coupling parameter.

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Design and Analysis of RF Section and Beam Wave Interaction for C Band 250 kW CW High Power Klystron

A. Modeling of Cavity in Superfish
The cavity designed is shown in figure and voltage and stored energy is obtained from various files generated by running this program. So, R/Q is calculated by the formula R/Q=V 2 /2ωU and value obtained is ~114 Ω.
Considerable interest has been shown in extending the bandwidth of the klystron amplifier, while retaining its high gain, stability and efficiency. The theoretical analysis of multi-cavity klystron operation has met with a number of difficulties owing to the complicated nature of modulation processes involved. Account must be taken, for example, of the interaction between non adjacent cavities. As a result, the design criteria for optimum performance, such as the number of cavities required, their spacing, design and detuning from the band center, the effects of space charge and the quality of

Results of Simulation
The present design employs four intermediate cavities to increase the gain as well as bandwidth by stagger tuning and penultimate cavity to increase the efficiency.

a. Output Cavity Design
The design of the output cavity is primarily influenced by the cavity R/Q which in present case is chosen to be 90. The loaded quality factor Q L is 72.

RF Section Simulation Using 1-D Code AJDISK
AJDISK is a 1-D large signal code developed by A. Jensen and is available in public domain. It is an ideal code for quickly estimating the basic design of klystron. Input needed to run the program include resonant frequency, Qs, R/Q and gap voltage of each cavity, axial distance between the gap centers, operating beam voltage, current and drive power. The output of the program includes gain, output power, cavity voltages, phase diagram and velocity dispersion diagram.
A typical output generated by the program for design of present tube is shown in figure 3.

RF Section Simulation Using Magic Code
MAGIC is particle-in-cell code developed by Mission Research Corporation, USA. The code is available both in 2D and 3D versions. It simulates actual electric and magnetic fields by tracing the outlines of RF cavities, drift tubes and pole pieces on closely spaced grids pushing thousands if simulated electrons through these simulated fields and iterating to convergence. The code is capable of designing electron gun and cavity as well.
Following figures show the results of RF-section simulation using MAGIC code.

A. Magic 2D Results for 360mm RF Section Length
After simulation of RF beam wave interaction in MAGIC 2D a power of 290KW is obtained as output, which goes in accordance with our desired power.

Conclusions
Simulation of RF cavities of 5GHz, 250 kW CW klystron has been done using POISSON and SUPERFISH CODES. Both codes results are well agreement. Beam-wave interaction simulation comparison carried out in AJDISK AND MAGIC 2D Codes. In both codes RF output power achieved greater to the desired 250 kW CW power for 5GHz Klystron. These results have been experimentally validated and well matched.