83 Annual Report IE 2012
83Annual Report IE 2012EC–Project EURATOM of FP7Contract FU07-CT-2007-00059/Fusion CSA/EURATOMMODELING AND SIMULATION OF GYROTRONS FOR ITERS Sabchevski1, M Damyanova1, I Zhelyazkov2, P Dankov2, P Malinov2,E Balabanova1, E Vasileva1 and R. Enikov11Emil Djakov Institute of Electronics,Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria,Association EURATOM-INRNE2Faculty of Physics, St. Kliment Ohridski University of Sofia,5 James Bourchier Blvd., 1164 Sofia, BulgariaAssociation EURATOM-INRNE1. Introduction: scope and mainactivities of the projectAs the most powerful sources ofcoherent radiation operating in acontinuous wave (CW) mode in thesub-terahertz frequency range (i.e., withmillimeterandsub-millimeterwavelengths) the gyrotrons are consideredas indispensable components of thesystems for electron cyclotron resonanceheating (ECRH) and electron cyclotroncurrent drive of magnetically confinedplasmas in various reactors (most notablyof the tokamak type) for controlledthermonuclear fusion [1, 2]. Additionally,they are used for startup (ignition),stabilization (e.g., NTM suppression andMHD control) and diagnostics of theplasma [3, 4]. It should also be noted thatthe gyrotrons are the only sources of RFheating, which can be both localized andsteerable. The ECH system of ITER, forexample, requires 24 MW installed RFpower (20 MW launched in the plasma) at170 GHz for heating and 3 MW at127 GHz for plasma startup. According tothe technical specification of the ITERproject, the requirements to the gyrotronsare: (i) output power not less than0.96 MW at the matching optic unit(MOU); (ii) output frequency of170 0.3 GHz; (iii) pulse length 3600 s;(iv) RF efficiency not less than 50 %; (v)Gaussian content of the wave beam greaterthan 95%; (vi) frequency of powermodulation 3 5 kHz; (vii) reliability notless than 95 %. The state-of-the-art of thegyrotrons for fusion is summarized in [5].Their high performance is a result ofseveral advanced concepts incorporated inthe design of the tubes, most notably:(i) internal mode converter; (ii) CVDdiamond output window; (iii) efficientcoupling of the gyrotron beam with thetransmission line system through a MOU;(iv) depressed collector; (v) LHe and LHefree cryomagnets, etc. Gyrotrons with anoutput power exceeding 1 MW (in therange 1.2 2 MW) represent well thecurrent power levels achieved worldwide[5, 6]. Among them is the coaxial170 GHz / 2 MW gyrotron developed bytheEGYC(EuropeanGyrotronConsortium, which includes CRPP, KIT,HELLAS, IFP-CNR) and is produced byThales Electron Devices (TED). Theshort-pulse (in the millisecond range)pre-prototype of this tube achieved at KITthe record power of 2.2 MW at 30 %efficiency without SDC (and 45 %efficiency at 2 MW) and 96 % Gaussianmode purity [4]. However, despite thesepositive results, serious problems ofdifferent nature have been encounteredduring the recent tests (internal tubefailure, operation on a wrong mode,parasitic and after-cavity oscillations,lower-than-expected efficiency, arching, to
84Selected Projectsmention just a few) [7, 8]. In order tosurmount these problems, it was decided in2012 (see, for example, Ref. [9]) to switchto the development of 1 MW / 170 GHzgyrotrons with a conventional (cylindrical)cavity using the experience gained duringthe design and operation of other similartubes, e.g., 1 MW / 140 GHz for the W-7Xstellarator [10]. At the end of this conciseintroduction to the subject of our research– powerful gyrotrons for fusion it shouldbe mentioned that despite the remarkableachievements demonstrated recently thereare many challenges and problems(physical, engineering and technological)that have to be addressed. They requirefurthertheoretical,numericalandexperimental investigations. In thisrespect, modeling and simulation, as wellas numerical experiments, are essentialtools for analysis, comparison andoptimization of different novel designs ofthe tube’s main subsystems and,eventually, for computer aided design(CAD) of the entire design.At present, the European gyrotroncommunity uses a great number ofstand-alone computer codes and severalproblem-oriented software packages fornumerical studies and CAD of namical system; quasi-opticalsystem) of powerful gyrotrons (see figure 1).In them, a wide variety of physical modelswith different levels of adequacy (rangingfrom self-consistent to phenomenological,time-dependent to static, etc.) isimplemented. Most of them however, arestatic and are formulated in a twodimensional coordinate space (2.5Dphysical models) and thus do not take intoaccount a number of factors (e.g., violationof the axial symmetry; misalignment of thecoils, electrodes and so on; nonuniformityoftheemission,space chargecompensation and many others). Ourresearch team has been involved in themaintenance and further refinement(improvement,optimization,andenrichment) of the available simulationtools (physical models and computerprograms), as well as in the developmentof novel ones. The work on this topic isbeing carried out in collaboration with theInstitute for Pulsed Power and MicrowaveTechnology at Karlsruhe Institute ofTechnology, the Association EURATOM–KIT (KIT-IHM) and the Centre deRecherches en Physique des sociationEURATOM–Confédération Suisse (CRPP-EPFL).The scope of the project (Task 2.1.2)encompasses all aspects of modeling andsimulation, namely: (i) theoretical work onthe formulation of adequate, informative(but still numerically traceable) physicalmodels taking into account as much aspossible physical factors and phenomena;(ii) selection of appropriate numericalmethods, programing libraries andenvironments for development of efficientalgorithms describing mathematically thephysical model; (iii) programming thecomputationalmodules(programimplementation of the algorithms);(iv) numerical experiments for testing andbenchmarking of the simulation tools, aswell as for analysis of concrete designs ofpowerful gyrotrons.Figure 1. Structure of the simulation tools andcomputational infrastructure for numerical studiesand CAD of gyrotrons.The work in the above-mentioneddirections follows a concept that hasalready been formulated in the precedinginvestigations [11, 12], but which has been
85Annual Report IE 2012subject to a steady and continuousdevelopmenteversince[13 18].According to this concept, the mostcharacteristic distinguishing features of thenext generation of codes are: (i) increasedphysical content (i.e., more physicalfactors and phenomena taken into accountincluding a transition from 2D to 3Dmodels); (ii) higher computationalefficiency (economical and optimized useof computational resources, such as runtime and memory); (iii) extensibility;(iv) portability to different platforms andoperating systems including execution ondifferent parallel computers.generator; the ASTRID finite elementsolver, a graphic system for visualization,a command language and interfacingmodules. DAPHNE is implemented as ascript written in ASTRID’s commandlanguage and includes the two modulesCFI (for calculation of the magnetic fieldof the coils of the tube) and PART (forintegration of the equations of particlesmotion) written in FORTRAN. The scriptinvokes successively both the particlepusher (PART) and the Poisson solver inan iterative loop until the processconverges to a self-consistent solution.2.2 ESRAY (KIT)2. Current status and functionality ofthe problem-oriented software packagesThe hierarchy and structure of thesimulation tools are presented in figure 1,together with the computational platformson which the different packages areoperational.2.1 DAPHNEDAPHNE package [14] (developed atCRPP-EPFL)isaprogrammingenvironment for optimization of EOS ofgyrotrons. It is based on an adequateself-consistent physical model (formulatedin 2.5D) which consists of a field part(a boundary value problem with Dirichletand Neumann boundary conditions for thePoisson equation that governs theelectrostatic potential distribution takinginto account the space charge) and adynamical part, which contains therelativistic equation of motion of chargedmacro particles representing the electronsof the beam. The computational region(2D meridional cross-section of an axiallysymmetric EOS) is discretized using astructured mesh with rectangular cells.DAPHNE is embedded in the ASTRIDproblem solving environment, whichincludes: a data base management systemformemoryanddatahandling(MEMCOM); a 3D adaptive meshESRAY (KIT) [14, 17] is also aproblem-oriented package for trajectoryanalysis (ray-tracing) of EOS based on afully relativistic 2.5D electrostatic physicalmodel.Itsmostcharacteristicdistinguishing features are: (i) an objectoriented program implementation in C ;(ii) an advanced mesh generator whichdiscretizes the computational domain witha great accuracy by structured boundaryfitted grids; (iii) versatile post-processingcapabilities and visualization of all scalarand vector physical fields by color maps;(iv) a fast own solver for the boundaryvalue problem by the finite differencemethod. The package consists of severalmodules: GRIDGEN (for geometrydescriptionandmeshgeneration),MAGGEN (for calculation of the magneticfield produced by a system of solenoids),ESRAYS (for iterative solution of theself-consistent field problem), and OVIS.The latter module serves as a GUI andpostprocessor that presents and visualizesthe results of the simulation.2.3 CAVITY (KIT)The problem-oriented software packageCAVITY (KIT) consists of a hierarchy ofcodes that begins with simple programs(e.g., for an analysis of the modespectrum; cold-cavity code, single-mode
86Selected Projectsself-consistent code) and culminates in themostsophisticatedself-consistentmultimode time-dependent code SELFT.Both the structure of the package and thephysical models implemented in itsmodules have been reviewed recently [17].The codes are written in FORTRAN andare invoked through a GUI. The GUI itselfis in fact a Tcl/Tk script for a Linux (Unix)bash shell that controls: (i) the interactionwith the codes, (ii) the specification of theinput data, and (iii) the visualization of theresults using a set of single commands inthe menu window.2.4 GYROSIMGYROSIM is a cal libraries and source codes ofvariouscomputationalmodules(standalone programs, subroutines, pre-,post-processing, and visualization codes)for solving a variety of problems pertinentto the simulation and CAD of gyrotronsusing a rich set of adequate physicalmodels [18]. Unlike the other packagesdescribed above, it is not, however,specialized to only one subsystem of thegyrotron tube. Rather, the individualcomponents of GYROSIM are designedfor simulation of all main subsystems ofthe gyrotron tube, notably: (i) the electronoptical system (EOS), (ii) the magneticsystem which includes the main magnetand an arrangement of additional coils,(iii) the electrodynamical system (resonantcavity), and (iv) the quasi-optical systemfor mode conversion and transmission ofthe radiation. It should be mentioned thatthe codes for numerical modelling of theEOS (GUN-MIG/CUSP) are based on a2.5D physical model, which is analogousto the one implemented in DAPHNE andESRAY, and, therefore, provides resultsthat are consistent and in a good agreementwith each other. Besides the SP,however,allowsmagnetron injection guns (MIG) with areversal of the magnetic field (e.g., amagnetic cusp) that form axis-encircling(aka uniaxial) beams to be simulated withan increased accuracy. Similarly, the codesof GYROSIM for simulation of theelectrodynamical system cover the samefunctionality as the CAVITY (KIT). At thesame time, there are some notabledifferences between them. For instance,the CAVITY (KIT) can treat bothconventional and coaxial resonators but atfundamental operation, while the cavitycodes belonging to GYROSIM arespecialized only to cavities without aninsert but can simulate operation at thesecond (and in the case of a large orbitgyrotron (LOG), even higher) harmonic ofthe cyclotron frequency. In its currentform, the GYROSIM is a heterogeneouspackage and includes components writtenin different languages (Fortran 77, Fortran90, C, C , SciLab), operational and/orportable to different computationalplatforms (ranging from laptops andworkstationstomainframeandsupercomputers), and executable ) operating systems(e.g., Unix, Linux, Windows, Cygwin).Another characteristic feature of thepackage is that it is being built following aconcept of extensibility which allows us toadd/replace easily different computationalmodules and in such a way modify boththe numerical algorithms and the physicalmodels implemented in the programs. Thelatest upgrade of GYROSIM package hasbeen carried out in parallel with thedevelopment of a novel module calledGO&ART (which stands for GeometricOptics and Analytic Ray Tracing). Itconsists of several codes (RAYS,COMODES, and TRACE) for analysis ofquasi-optical components (Vlasov andDenisov type launchers, reflectors andphase-correcting mirrors, etc.), as well assystems based on them (e.g., internal modeconverters and transmission lines).
87Annual Report IE 20122.5 GYREOSSInitially, GYREOSS was conceived as apackage of codes for simulation of EOSusing a physical model formulated in threespace dimensions in order to take intoaccount the departure from axial symmetrydue to various misalignments (for instanceof the electrodes, of the magnetic coils,etc.) and non-uniformities [15]. Its initialversion was implemented using the Gmshpackage for meshing, pre- and postprocessing and GetDP as a solver. In therecent years, however, GYREOSS hasevolved as a test bench for experimentingwith different numerical methods, solversand algorithms in 3D aiming at the finalgoal – a parallel 3D code for numericalsimulation and CAD of EOS of gyrotrons.The latest version of GYREOSS is beingdeveloped using the FreeFEM problemsolvingenvironmentandmedit(a scientific visualization software) but thecompatibility with Gmsh is preserved andthe latter can be used for generation andoptimization of the tetrahedral mesh(alongside with the mesher embedded inFreeFEM), as well as for post-operation,post-processing and visualization of thesolution. As an illustration, some meshesgenerated and optimized by Gmsh andused in the recent numerical experimentsare shown in figure 2.In 2012, a novel electrostatic fieldsolver of the GYREOSS software packageFigure 2. Surface meshes representing theelectrodes of a coaxial gyrotron (2 MW/170 GHz)simulated by GYREOSS.was developed and tested. It isparameterized in such a way as to provideconvenient data structures of theelectromagnetic fields at the currentparticle positions in both 2D and 3D.Figure 3 presents several screenshots thatillustrate the visualization capabilities ofGYREOSS. Figure 3a shows a map of theelectrostatic potential distribution obtainedin one of the test runs. The correspondingelectrostatic field is shown in figure 3b.Figure 3. Electrostatic potential distribution (a);equipotential lines over the mesh (b); map and avector representation of the electrostatic field nearthe emitting ring of the cathode (c), in a meridionalcross-section of a coaxial magnetron injection gun(MIG) of the studied 2 MW/170 GHz gyrotron.Another important task pursued during2012 was the development of an efficientmodule for integration of the relativisticNewton–Lorentz equations of motion ofbeam electrons (usually referred to as a“particle pusher” aka “particle mover”)formulated in 2D and 3D. It uses the datastructure of the electromagnetic fieldvalues at the current particle positions,provided by the novel field solverdescribed above and realized with anintended prospective parallelization of the
88Selected ProjectsPIC algorithm of GYREOSS. As apreparation, different methods for particletracing were considered and analyzed.Among them were the schemes of Boris(Tajima’s Implicit Method), Boris–Bunneman, Runge Kutta 4th ordermethod, Verlet’s method, and thepredictor corrector method. As manyresearchers did before us, and havingevaluated all important factors (accuracy,stability, CPU time etc.), we finallyselected the leapfrog method of therelativistic Boris Bunneman scheme. Thealgorithm realized is convenient because itrequires only one force evaluation per timestep and needs memory for storage of onlyone set of coordinates and velocities foreach particle. It should be noted, however,that several other advanced schemes(e.g., Lorentz invariant advance) deserveconsideration and we plan to study them aswell. We also intend to implement anadaptive calculation of the optimal timestep (for an arbitrary gyro-frequency),which will minimize the consumed CPUtime, while preserving a sufficientaccuracy. The more radical optimization,however, is expected after realization of aparallel (multithreaded) implementation ofthe PIC algorithm of GYREOSS. Asmentioned above, a preparation for suchparallelization is in progress now andincludes studies on MPI, multithreadingand building of a computing clusters usingas nodes the workstations of the availablecomputational infrastructure at IE-BASbefore going to the Pleiades cluster forfull-scale simulations.As an illustration, in figure 4 we presentseveral trajectories traced in a coaxialmagnetron injection gun (CMIG) for a2 MW/170 GHz gyrotron calculated byGYREOSS using its novel particle mover.3. Computational platforms used forcode maintenance and developmentAll packages outlined above (CAVITY,ESRAY, GYROSIM, GYREOSS) areinstalled and are operational on the work-Figure 4. Geometry of the coaxial magnetroninjection gun (CMIG) of a 2 MW/170 GHzgyrotron (black color) and electron rays (red color),traced by the novel relativistic particle pusher ofthe GYREOSS package.stations of the Bulgarian research team(see figure 1), except DAPHNE, which isavailable to us for remote execution andmaintenance on the PLEIADES2 clusterfrom Sofia. Since the outstandingperformance of PLEIADES2 is wellknown, we will mention only the basiccharacteristics of the most powerful of ourworkstations. ITER I has two CPU AMDOpteronTM Dual Core 275, 2.2 GHz andRAM 4 GB DDRAM with a MBSupermicro -Dual Opteron and SVGANvidia GeForce 6600 TD. The workstationITER II has 2 CPUs Intel Xeon X5680,3.33 GHz,12 MB cache, 6 Cores; memory4 4GBDDR-31333.Onbothworkstations the operating system isUbuntu 10.04 (lucid), Kernel Linux2.6.32-41-generic. Although some of them(e.g.,DAPHNE,ESRAY-IHM,CAVITY-IHM, and various componentsof GYROSIM) are well validated,benchmarked and debugged, they areundergoing constant adaptation andupgradetotheever-changingcomputational environments (hardware,operating systems, novel versions of thecompilers and numerical libraries).Alongside with the maintenance of thesecodes and their usage in numericalexperiments, we are working on the furtherdevelopment of the GYREOSS andGYROSIM packages.
89Annual Report IE 20124. Conclusions and outlookTheproblem-orientedpackagesoutlined in the previous section are undercontinuousdevelopmentandimprovement. Recently, they were used ina series of numerical experiments carriedout to study the designs of powerfulgyrotrons that are under considerationand/or development at present. Thesimulations conducted give a deeperphysical insight into the operation ofhigh-performancemegawatt-classgyrotrons and are good benchmarks thatdemonstrate the improved capabilities andfunctionality of the upgraded codes.Moreover, these results suggest somefurther experiments for more detailedstudy of the correlation between thebeam-quality parameters and efficiency,on one hand, and the particular design(configuration of the electrodes, tailoringof the magnetic field, etc.), on the other. Itis expected that the novel and upgradedversions of the simulation packages w
systems for electron cyclotron resonance heating (ECRH) and electron cyclotron current drive of magnetically confined plasmas in various reactors (most notably of the tokamak type) for controlled thermonuclear fusion [1, 2]. Additionally, the
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