Chauhan, N.

Kamakshi, S.

Kartikeyan, M.V.

Kumar, A.

Mittal, A.

Thumm, M.K.

Wagner, D.

Kartikeyan, M. V.

Thumm, M. K.

KITopen

Design and Optimization of Non-linear Tapers forHigh Power GyrotronsNarendra Chauhana, S. Kamakshia , Arun Kumara, Ankush Mittala, Dietmar Wagnerb,M.V. Kartikeyana*, and M.K. Thummc,d(*kartik@ieee.org)aDepartment of Electronics and Computer EngineeringIndian Institute of Technology Roorkee, Roorkee - 247 667, Uttarakhand, IndiabMax-Plank-Institut für Plasmaphysik EURATOM-IPP, Boltzmannstr. 2D-85748 Garching, GermanycForschungszentrum Karlsruhe, Association EURATOM-FZKInstitut für Hochleistungsimpuls- und MikrowellentechnikPostfach 3640, D 76021 Karlsruhe, GermanydUniversitaet Karlsruhe, Institut für Hoechstfrequenztechnik und Elektronik,Kaiserstraße 12, D 76131 Karlsruhe, GermanyAbstractAbstract. In this paper, the design and optimization of non-linear taper connecting the output section of the cavityresonator to the uniform waveguide section for high power gyrotrons is presented. The design of a non-linear taper ofa 42 GHz, 200 kW CW gyrotrons operating in the TE0,3 mode with axial output collection has been taken as a casestudy. The taper synthesis has been carried out using conventional taper design procedures and analysis is carriedout using a dedicated scattering matrix code. In addition, an improved particle swarm optimization – an evolutionaryoptimization algorithm – is presented and used for the design optimization of non-linear taper.I. IntroductionGyrotron output system consists of an output taper which connects the interaction region with the main waveguide system, aquasi-optical  mode  converter,  and  the  RF  window  [1].  The  requirement  of  a  taper  in  gyrotrons  is  good  match  with  thesuppression of spurious modes. Various taper designs [2] such as exponential taper, triangular taper, Klopfenstein taper can beemployed for matching purpose. In this work, we have used a raised cosine taper profile as it yields less mode conversion thanthe Klopfenstein profile or an exponential tape [3]. The design and optimization of raised cosine nonlinear taper is carried out fora specific 42GHz, 200kW, CW Gyrotron operating in the TE0,3 mode with axial output collection. The scattering matrix methodis very fast and accurate for taper analysis. In this work, the analysis of the taper was carried out using a dedicated scatteringmatrix  code  [4].  Particle  Swarm Optimization  (PSO),  developed  by  Kennedy  and  Eberhart  [5]  is  a  simple,  effective  andpromising  method  used  for  search  and  optimization  in  multidimensional  feature  space.  The  feasibility  of  simple  PSO  isillustrated in [6] for high-power microwaves control applications. In this paper, an improved particle swarm optimization methodis presented and used for the design of non-linear tapers.II. Particle swarm optimizationParticle swarm optimization (PSO) is a population based stochastic optimization technique developed by Eberhart and Kennedy[5].  In this  algorithm, group of potential  solutions,  known as particles  are  flown through the search space in order  to getoptimum solution. The ith particle in the swarm (a population of particles) is represented as Xi = (xi1, xi2, …, xiD),  and itsvelocity is given by Vi = (vi1, vi2, …, viD). The best previous position of each particle is given as Pi = (pi1, pi2, …, piD). The bestparticle among all particles is represented by symbol ‘g’. The velocity and position of each particle is updated using followingrelations:(1a)(1b)where c1 (cognitive constant) and c2 (social constant) are two positive constants, rand() is a function to generate random numberbetween 0 and 1, and w represents inertia weight which is used to control between local and global search.The ability of PSO in exploring global optima is much dependent on the choice of parameters such as c1, c2 , w, and Vmax.Various experiments for the selection of optimum parameters are demonstrated in [7]. In our experiment, linearly decreasingDesign of Nonlinear Taper for high power Gyrotrons1 von 4 15.10.2015 14:28inertia weight (w) as proposed in [8] is used. The maximum velocity in each dimension is also restricted to Vmax= 0.25·Xmax.The value of cognitive acceleration constant (c1) and social acceleration constant (c2) are fixed at 2.0 which are suggested as bestin most experiments. In this paper, we have experimented PSO with 10 and 30 population sizes for 100 and 300 iterationsrespectively.An improved  PSO algorithm for  constrained  optimization  is  used  in  this  work.  The  algorithm is  the  modification  of  thealgorithm  presented  by  Hu  and  Eberhart  [9]  for  handling  constraints  efficiently.  It  includes  3  modifications:  dynamicinitializations particles and velocity both within specific range, penalty based approach for constraints handling and imposingrestrictions to bound constraints by the range of range of parameters. The advantage of the proposed modifications is that theinitialized particles need not satisfy all the constraints, thus making the algorithm easy work and efficient to handle designconstraints. The proposed algorithm used is shown in Fig. 1 with the modification highlighted.Figure 1. Improved Particle swarm optimization algorithm for constrained optimization.III. ExperimentIn this paper, the design of raised cosine taper for 42 GHz, 200 kW, CW gyrotrons is performed. We consider four designparameters of the nonlinear taper namely – length of taper (L), radius of taper at output end (r2), number of sections (n), andgamma (γ) while keeping radius of taper at input end (r1) constant. The range of design parameters considered for the design arementioned  in  Table  1.  The  objective  for  the  design  considered  was  to  obtain  maximum  transmission  coefficient  (i.e.s21-parameter).Design parameter RangeLength (L) 200~350 mmRadius at output end (r2) 35~45 mmNumber of sections (n) 50~500Gamma (γ) 0.1~1.0Table 1: Range of design parametersThe optimization for the design parameters was carried out using improved PSO as presented in previous section with swarmsize 30 for 300 iterations. We have also observed the effects of varying gamma parameter and radius at the output end of thetaper (a2) on the transmission coefficient. The effect of parameter gamma (γ) on the taper synthesis and transmission coefficientis shown in Fig. 2, while the effect of radius (at output end) on the taper synthesis and transmission coefficient is shown in Fig.3. A transmission coefficient of 99.86 was obtained using optimized design parameters. The optimized taper was obtained withlength 310.67 mm, output end radius of 35 mm, with 382 no. of sections, and 0.527 value of gamma parameter.Design of Nonlinear Taper for high power Gyrotrons2 von 4 15.10.2015 14:28Figure 2. Effect of gamma parameter on the synthesis of raised cosine taperFigure 3. Effect of radius (r2) on the synthesis of raised cosine taperIV. ConclusionsAn improved particle swarm optimization algorithm is presented and used for the design of raised cosine non-linear taper forspecific high power gyrotrons. A dedicated scattering matrix code was used for the fast and accurate analysis of taper duringdesign process. The selection of PSO parameters was carried out in accordance with previous experimental investigations. Theoptimized results show the best matching obtained with the taper which shows effectiveness of the method. The time required forthe optimization was 30 minutes approximately.References:[1.] MV Kartikeyan, E Borie, and M Thumm, Gyrotrons - High Power Microwave and Millimeter Wave Technology. Springer-V[2.] R E. Collin, Foundations for Microwave Engineering. McGraw-Hill, New York, (1966).[3.] W.G.Lawson, Theoratical evaluation of non-linear tapers for a high power gyrotrons. IEEE Transactions on Microwave Theo[4.] D. Wagner, M. Thumm, G. Gantenbein, W. Kasperek, and T. Idehara, Analysis of a complete gyrotrons oscillator using the s[5.] J. Kennedy, and R. Eberhart, Particle swarm optimization. Proceedings of the 4th IEEE Intemational Conference on Neural [6.] Alexandr A. Bogdashov, and Yury V. Rodin, Mode Converter Synthesis by the Particle Swarm Optimization. Int. J. Infrared[7.] Y. Shi, and R. Eberhart, Parameter selection in particle swarm optimization. Proc. of 7th Annual Conference on Evolution Co[8.] Y. Shi, and R. Eberhart, Empirical study of particle swarm optimization. Proceedings of the 1999 Congress on Evolutionary [9.] X. Hu, and R. Eberhart, Solving constrained nonlinear optimization problems with particle swarm optimization. ProceedingsDesign of Nonlinear Taper for high power Gyrotrons3 von 4 15.10.2015 14:28Design of Nonlinear Taper for high power Gyrotrons4 von 4 15.10.2015 14:28

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