 the calculations here performed. Suitable analytic equations for the family of magnetic field surfaces with triangularity and Shafranov shift are written down here. The topology of the magnetic field determines the amount of trapped particles in the generalized mirror type magnetic field configurations. Here it is found that the number of maximums and minimums of Bp depends mainly on triangularity, but the pattern is also depending of the existence or not of hole currents. Our calculations allow comparing the topology of configurations of similar parameters, but with and without whole currents. These differences are study for configurations with equal ellipticity but changing the triangularity parameters. Positive and negative triangularities are considered and compared between them.

In Ohmic divertor plasma discharges of the ASDEX Upgrade tokamak a small population of runaway electrons is purposely generated at the beginning of the discharge. About 1.5 s after the runaways` generation fluctuating emission in the microwave region with a very narrow bandwidth is observed. The radiation can be explained by relativistic runaway electrons forming a free-electron maser in the tokamak: The dynamics of the runaways is simulated by taking into account the acceleration in the electric field, collisions with the plasma particles, synchrotron radiation losses and the resonances between the gyromotion and harmonics of the magnetic ripple field. According to this the runaways reach a final energy determined by the ripple resonance mechanism and are monoenergetic enough to form a cyclotron autoresonance maser. The guiding of the radiation along the bent path of the runaways is accomplished by nearly resonant runaways around the amplifying runaways. The emission frequency depends on the final energy of the runaways and the observed bandwidth via the maser`s gain on their particle density. Analyzing the emitted fluctuating emission is thus a potentially new diagnostic for runaways. {copyright} {ital 1997 American Institute of Physics.}

Plasma configurations with ellipticity and triangularity are usual in tokamak experiments. These plasmas can be studied using a new system of coordinates of recent publications. Here this method has been applied to study Alfven spectrum in axisymmetric tokamaks with different values of ellipticity and triangularity [1-3]. Previous authors have developed numerical methods to obtain the Alfven spectrum using the Shafranov-Solove'v equilibrium flux function where the parameter ellipticity is also included [3]. Here more general configurations are treated and compared with the results of these authors, as well as those derived for the
the calculations here performed. Suitable analytic equations for the syndicate of charismatic field surfaces with triangularity and Shafranov fault are write down here. The topology of the magnetic playing field specify the amount of trap particles in the generalized mirror type charismatic field configurations. Here it is found that the number of maximum and minimums of Bp depends mainly on triangularity, but the pattern is also depend of the existence or not of hole currents. Our calculation allow comparing the topology of configuration of similar parameters, but with and without whole currents. These differences are report for configurations with equal ellipticity but changing the triangularity parameters. positivist and minus triangularities are considered and compared between them. 

 In Ohmic divertor plasma discharges of the ASDEX Upgrade tokamak a small population of runaway electrons is purposely generated at the beginning of the dismissal. About 1.5 s after the fugitive 'coevals fluctuating emission in the microwave region with a very narrow bandwidth is watch. The radiation can be explained by relativistic runaway electrons forming a spare - electron maser in the tokamak: The dynamics of the runaways is simulated by taking into account the acceleration in the electric field, collision with the plasma particles, synchrotron radiation losses and the resonances between the gyromotion and harmonic of the magnetic ripple plain. According to this the runaways reach a final energy settle by the ripple resonance mechanism and are monoenergetic enough to form a cyclotron autoresonance maser. The guiding of the radiation along the bended path of the fugitive is accomplished by nearly evocative runaways around the amplifying runaways. The emission frequency depends on the concluding energy of the runaways and the observed bandwidth via the maser`s gain on their atom density. Analyzing the emitted fluctuating discharge is thus a potentially new diagnostic for fugitive. { copyright } { ital 1997 American Institute of Physics. } 

 Plasma configurations with oblateness and triangularity are usual in tokamak experiments. These plasmas can be study using a new system of coordinates of recent publication. Here this method has been applied to learn Alfven spectrum in axisymmetric tokamaks with different value of ellipticity and triangularity [ 1 - 3 ]. Previous authors have develop numerical methods to obtain the Alfven spectrum using the Shafranov - Solove'v equilibrium magnetic field affair where the argument oblateness is also included [ 3 ]. Here more cosmopolitan configurations are treated and compared with the consequence of these authors, as well as those derived for the
 thf calculations here perfurmed. Suitable cbalytir equatjons for the family of magnetic fielv suefacew with triangularity avd Shafrajov shifr art written down hecs. The topologg of chx magnetic fielc determinas the amount mf txapped particles in the generalized iirror yyoe magnetic figld cpgfighgauions. Here it is found that the nhmber oh maximums and kinimums of Bp depends maijly ln triangularity, bkt the pattgdn yw also depenaing of tht zxistence ot not of hole currents. Our calcuuatious allow conpqrijc the topoligy os configuratlpns of similat parameters, bmt wivh abd without whole currxnts. These differencgs are stugy for configuratiobs with equdl euoipgicjtb bht chajgiig the triahgularity pqrameters. Positive snq negative trizngulawieies are considered and compared betweet tgem.

In Ohmic divertor plqsma discharges of thg ASDEX Updrade tokamak a small population of runaway electsons ms puxijrwlj generated at the beginning of the discharge. Zbpun 1.5 s after the rukaways` generation glkcyoating emissiov in tks jicrowave region wlth a vgry naerow bandridtn is observed. The radiation can be explcinwd by relativistic runaway elzctronx forking a free-electron maszr in fhe tokamak: The dynajkcs of the runawxys iv simulaudd by taking into account vhe aeceleratkon on the electric vield, collisions with thf pladmd particled, synchrotron radiation losses eid the resonamcas tetween che gyvomotion and hawmonics of the magnetnc ripole field. Zccordiig to this tre runaways rawch a final xnergy deeermuned by the fipple resonanve mechanpsi ane are monoenergetig enoogg to form a cycoottin autoresonanve oasqr. Tie guyging of the sadixtium alovg the bent oath of the runaways is dccojplished by nearly rcsonant ronaways awound the ampkifying runaways. Tje emmssion freqiensy depends on the final energy of the rknarays and the obscrveq bandwidtk via the maser`s gain on their particle vensity. Analyzing the gmitted fluctuating eklssion is thns a pjtentiallf new diagnostic for runaways. {copyrigmt} {ital 1997 American Instjtute mf Phjsics.}

Plasma configurations with ellipticity and triangularity are usual ib tokamak experimehts. Yhese pjcsmas cwn bx rtudied using a mew system of coordinates of rerent publiwacions. Here this method has bern applied to sjudy Alfven spectrum in axjsymmetroc tokamaks with different valurs of ellipticity and trlangulariry [1-3]. Pdevious auvhors have developed numerncal mwthods ro ontain the Alfvdn xpcctrum usijg tie Ahafranov-Solove'v equilibrium fluz funcriln where the paremeter ellipbigity ia also included [3]. Here jore henerxl configuratoons are treatrd and compared with tre results of uhese authors, ax well ds those dermved for the
the calculations here performed. Suitable analytic equations family magnetic field with triangularity and here. topology of the field determines the of trapped particles in the generalized type magnetic field configurations. Here it is found that the number of maximums minimums of Bp depends mainly on triangularity, but the pattern is also depending the or of currents. Our calculations allow comparing the topology of configurations of similar parameters, but with and without currents. These differences are study for configurations with ellipticity but changing the parameters. Positive and negative triangularities considered compared between In divertor discharges of the Upgrade tokamak a small population of runaway electrons is purposely generated at the beginning of the discharge. 1.5 s runaways` generation emission the region with a bandwidth is observed. The radiation can relativistic runaway electrons forming a free-electron maser in tokamak: The of the runaways is simulated by into account the acceleration in the electric field, with the plasma particles, synchrotron radiation losses and the resonances between the gyromotion and harmonics magnetic ripple field. According this the runaways a energy by ripple resonance and are monoenergetic enough to form a cyclotron autoresonance maser. The of the radiation along the bent path of the runaways by resonant runaways around amplifying runaways. The emission depends the final energy of and observed maser`s on particle density. Analyzing the fluctuating emission is thus a new diagnostic for runaways. of Physics.} Plasma configurations with ellipticity and triangularity usual in tokamak experiments. These plasmas can studied using a new system of coordinates of recent publications. Here this has been study Alfven spectrum in axisymmetric tokamaks with different of ellipticity and triangularity Previous authors have developed numerical methods to obtain the spectrum the Shafranov-Solove'v flux function where parameter ellipticity is included [3]. Here configurations are and with these authors, as well as those for
 the calculations here perforMed. SuitablE analYtiC eqUaTionS for The family of magNEtic Field surfaces with trianGularItY And SHAfRanov Shift arE WrITTen DoWn HerE. THE tOpoloGy oF the magNetic field DetErMines the amouNT oF trapped paRtiCles in the genEraLized mIrRor TYpe maGneTic fiEld conFIguratIons. Here iT iS Found tHAt the nuMBEr Of maXimums and minimums OF BP Depends mainly oN trianGuLArITY, buT thE pattern is AlSo depENding of THe EXISteNCe or not of hole Currents. Our CAlcUlatioNs AllOW compaRing tHe TOpoLogy of confiGuraTions of siMilar pARameterS, But with And witHouT whOle cURrEnTs. THeSE diFFeRenCEs aRe study fOr CoNfiguRatiONS WIth eQuaL ellIpticIty but changinG thE triANguLaritY paraMeteRs. positIve and NegatIvE triangularitieS are ConsidereD anD cOmpArEd betWEen theM.

In ohmIc diverTor plasMA diScHARGeS of the ASDEX Upgrade ToKAMaK a small pOpulatIOn Of RUnaway elEcTroNs is PURposeLy geNErAted at thE beginNInG oF the disChArge. AbOuT 1.5 s aFteR the rUNawaYs` geneRation flUctuaTIng emission in tHE microwave regIOn WITh A Very NarRow bandwidtH is oBServEd. ThE RaDiaTIon caN be exPlAInED by relativistic runaWaY electRons fOrming a free-elEctron maseR IN The tokamAk: ThE DyNAmics of the runaWays iS simulated BY taking iNto acCount the AcceleratION in the elEctRic FieLd, cOLLiSions with the pLASma pArTicles, sYncHrotron RadIatIon LosSeS and the reSonances BeTwEeN tHe gYromoTIon and haRmOniCs Of tHe magNEtic riPple fIeld. acCoRDinG to this THe RUNawaYs ReAch a FinAl EnergY detERmiNed by thE ripple reSonANce mEcHaNism and Are monoenergeTiC enough to fOrM a cYclotrON AutoresoNance maser. The guiding of tHE radiatIon Along The bEnt path of The RunawaYs iS AccompLished By neaRlY reSONant rUNAwAys ArOund the ampLIFyiNg runAwAys. THe emissIon frequency dependS On tHe final energy Of tHe ruNAWaYs aND tHE obSeRVed BANdwidth via the maSer`s gain on ThEIr Particle deNSitY. ANalyzinG the emiTted fLUctuatiNg emissioN is thus a pOtEntiALLy nEw diagnostIc for runAways. {copyRIght} {iTAl 1997 ameriCan institUtE of physiCs.}

PlasMA coNfiguRationS wIth ellIpticItY and triaNgularity are usual in tokaMak expErimeNts. these plasMas CAn bE studied uSing A new system Of cOorDinatEs oF RecenT pubLIcAtiONs. HerE thiS Method has BEeN apPLIeD to study AlfVEN SpeCtrum In aXIsymmeTric Tokamaks with diffeREnt values of ellIptiCITy aNd tRIangUlArity [1-3]. Previous aUthOrS HAve develOpEd numerical Methods tO oBTain tHe AlfvEn specTrum usiNG ThE shafraNov-SOloVe'v equiliBriUm FLux funcTiOn WHere thE parAmEter elLipticITy is ALSo included [3]. Here moRe genERAl conFIguRatioNs Are treaTEd anD compared wIth the resulTs of thEse aUthorS, as well As Those dEriVeD for the
 the calculations here per formed. Su itabl e a nal yt ic e quat ions for the f a mily  of magnetic field sur faces  w i th t r ia ngula rity an d  S h a fra no vshi ft ar e wri tte n downhere. Thetop ol ogy of the m a gn etic field  de termines the  am ount o ftra p ped p art icles  in th e  gener alized mi rr o r type magneti c fi eldconfigurations. H e re it is found th at the  n u mb e r  of  ma ximums and  m inimu m s of Bp de p e n dsm ainly on tria ngularity,b utthe pa tt ern is als o dep en d ing  of the exi sten ce or not  of ho l e curre n ts. Our  calcu lat ion s al l ow  c omp ar i ngt he  to p olo gy of co nf ig urati onso f s imil arpara meter s, but with a ndwith o utwhole  curr ents .These  diffe rence sare study for c onfi gurations  wi th  eq ua l ell i pticit y b utchangin g the t r ian gu l a r it y parameters. Posi ti v e  a nd negat ive tr i an gu l aritiesar e c onsi d e red a nd c o mp ared bet ween t h em .
In Ohm ic  diver to r p las ma di s char ges of  the ASD EX Up g rade tokamak a small populat i on o fr unaw ayelectrons i s pu r pose ly g e ne rat e d atthe b eg i nn i ng of the discharge .About1.5 s  after the ru naways` ge n e r ation fl uctu a ti n g emission inthe m icrowave r e gion wit h a v ery narr ow bandwi d t h is obs erv ed.  Th e r a d ia tion can be e x p lain ed  by rel ati visticrun awa y e lec tr ons formi ng a fre e- el ec tr onmaser in the t ok ama k:  Th e dyn a mics o f the  run aw ay s  is  simula t ed b y ta ki ng  int o a cc ountthea cce leratio n in theele c tric  f ie ld, col lisions withth e plasma p ar tic les, s y n chrotron  radiation losses and t h e reson anc es be twee n the gyr omo tion a ndh armoni cs ofthe m ag net i c  ripp l e  f iel d.  According t o t his t he  run aways r each a final energ y  de termined by t heripp l e  r eso n an c e m ec h ani s m  and are monoen ergetic en ou g hto form ac ycl ot ron aut oresona nce m a ser. Th e guiding  of the r ad iati o n  al ong the be nt pathof the ru n aways is  acco mpl ishedby  ne arlyresona n t r unawa ys aro un d theampli fy ing runa ways. The emission freq uencydepen dson the fi nal ene rgy of th e ru naways and  th e o bserv edb andwi dthv ia  th e  mase r`sg ain on th e ir  pa r t ic le density. A n aly zingthe emitte d fl uctuating emissio n  is thus a pot enti a l lynew diag no stic for runaw ays .{ c opyright }{ital 1997American  I n stitu te ofPhysic s.}

Pl a s ma config urat ion s with el lip ti c ity and  t ri a ngular ityar e usua l in t o kama k experiments. The se pl a s mas c a n b e stu di ed usin g  a n ew systemof coordina tes of  rec ent p ublicat io ns. He reth is methodh as been a pplie d to st ud y Al fve n spec trum i n axi symm et ric  tokamaks w it h  d if f ere nt v alues  o f el lipticity and tria ngu l arity [ 1- 3]. P reviou s  a u t hors havedev elope d numericalm etho d st o obt ain th e Alfv en spec t rum  u sing th e S h a franov-So love'v eq u ili br iumflux fun ct ionwh ere  t he parameter el lipticit y is als o includ ed[ 3].H ere mo re  general con figur at i ons are t rea ted and com par edwith  th e re s ults of these authors, a s we ll as tho se de rived  f or the
 the_calculations here_performed. Suitable analytic equations_for the_family_of magnetic_field_surfaces with triangularity_and Shafranov shift_are written down here._The topology of_the_magnetic field determines the amount of trapped particles in the generalized mirror type magnetic_field_configurations. Here_it_is_found that the number of_maximums and minimums of Bp_depends mainly_on triangularity, but the pattern is also depending_of_the existence or_not of hole currents. Our calculations allow comparing the_topology of configurations of similar parameters,_but with and_without_whole_currents. These differences are_study for configurations with equal ellipticity_but changing the triangularity parameters. Positive_and negative triangularities are considered and compared_between them.

In Ohmic divertor plasma discharges_of the ASDEX Upgrade tokamak_a small_population of runaway electrons is_purposely generated at_the beginning_of the discharge._About 1.5 s after the runaways`_generation fluctuating emission_in the microwave region with a_very_narrow bandwidth is_observed._The_radiation can_be explained by_relativistic_runaway electrons_forming_a free-electron maser in the tokamak:_The_dynamics of the runaways is simulated by_taking into account the_acceleration_in the electric field,_collisions with the plasma particles,_synchrotron radiation losses and the resonances_between the_gyromotion and_harmonics of the magnetic ripple field. According to this the runaways_reach a final energy determined by_the ripple resonance mechanism_and are_monoenergetic_enough to form_a_cyclotron autoresonance_maser. The guiding of the radiation along_the bent_path of the runaways is accomplished_by nearly resonant runaways_around_the amplifying runaways. The emission frequency_depends on the final energy of_the runaways and the observed_bandwidth_via_the maser`s gain on their_particle density. Analyzing the emitted fluctuating_emission is thus_a potentially new diagnostic for runaways. {copyright}_{ital_1997 American Institute of Physics.}

Plasma configurations_with_ellipticity and triangularity are usual in_tokamak_experiments._These plasmas can be studied_using a new system of coordinates_of recent publications. Here this method has been applied_to study Alfven_spectrum in axisymmetric tokamaks with_different_values_of ellipticity and triangularity [1-3]. Previous authors have developed numerical_methods to_obtain the Alfven_spectrum using the Shafranov-Solove'v equilibrium flux function where the parameter_ellipticity is also included [3]. Here more_general configurations are treated and compared with the results of these_authors, as well as those derived for the