 balanced currents are thought to be thermoelectric in origin.

Tokamak plasmas are routinely observed to rotate even in the absence of an externally applied torque. This ``intrinsic'' rotation exhibits several robust features, including rotation reversals with varying plasma density and current and rotation peaking at the transition from low confinement to high confinement regimes. Conservation of toroidal angular momentum dictates that the intrinsic rotation is determined by momentum redistribution within the plasma, which is dominated by turbulent transport. The turbulent momentum transport, and thus the intrinsic rotation profile, is driven by formally small effects that are usually neglected. We present a gyrokinetic theory that makes use of the smallness of the poloidal to total magnetic field ratio to self-consistently include the dominant effects driving intrinsic turbulent momentum transport in tokamaks. These effects (including slow radial profile variation, slow poloidal turbulence variation, and diamagnetic corrections to the equilibrium Maxwellian) have now been implemented in the local, delta-f gyrokinetic code GS2. We describe important features of the numerical implementation and show numerical results on intrinsic momentum transport that are qualitatively consistent with experimental rotation reversals.

A non-intrusive method for inducing a radial electric field (Er) based on electron ripple injection (ERI) is under development by the Princeton CDX-U group. Since Er is known to play an important role in the L-H and H-VH mode transition, it is therefore important to develop a non-intrusive tool to control the Er profile in tokamak plasmas. The present technique utilizes externally-applied local magnetic ripple fields to trap electrons at the edge, allowing them to penetrate towards the plasma center via ∇B and curvature drifts, causing the flux surfaces to charge up negatively. Electron cyclotron resonance heating (ECRH) is utilized to increase the trapped population and the electron drift velocity by raising the perpendicular energy of trapped electrons. The temperature anisotropy of resonant electrons in a tokamak plasma is calculated in order to investigate effects of ECRH on electrons. Simulations using a guiding-center orbit model have been performed to understand the behavior of suprathermal electrons in the presence of ripple fields. Examples for CDX-U and ITER are given.

Runaway electrons (RE) resulting from the violent termination of tokamak plasmas pose a serious threat to ITER due to the very high energies they can reach and deposit on the plasma facing components. Most of the current modelling
balanced currents are thought to be thermoelectric in origin. 

 Tokamak plasmas are routinely note to revolve even in the absence of an externally applied torque. This '` intrinsic" rotation expose several robust feature, admit rotation reversals with change plasma density and current and rotation peaking at the conversion from low confinement to gamey parturiency regimes. Conservation of toroidal angular momentum dictates that the intrinsic rotation is determined by momentum redistribution within the plasma, which is dominated by turbulent conveyance. The turbulent momentum transport, and thus the intrinsic rotation visibility, is driven by formally small effect that are usually neglect. We present a gyrokinetic theory that makes use of the smallness of the poloidal to total charismatic field ratio to self - consistently include the dominant effects drive intrinsic turbulent momentum transport in tokamaks. These effects (including slow radial profile variation, dense poloidal turbulence variation, and diamagnetic corrections to the balance Maxwellian) have nowadays been implemented in the local, delta - f gyrokinetic code GS2. We describe important feature of the numeric implementation and show numeric results on intrinsic momentum transport that are qualitatively consistent with experimental rotation reversals. 

 A non - intrusive method for inducing a radial electric airfield (Er) based on electron ripple injection (ERI) is under development by the Princeton CDX - U group. Since Er is known to play an authoritative role in the L - H and H - VH manner transition, it is therefore important to develop a non - intrusive tool to see the Er profile in tokamak plasmas. The present technique use externally - applied local magnetic ripple fields to trap electron at the edge, allowing them to penetrate towards the plasma center via ∇B and curvature drifts, cause the flux surface to charge up negatively. Electron cyclotron plangency heating (ECRH) is utilize to increase the trapped population and the electron drift velocity by raising the perpendicular energy of trap electrons. The temperature anisotropy of resonant electrons in a tokamak plasma is calculated in order to investigate effects of ECRH on electrons. Simulations using a steer - center orbit mannequin have been performed to understand the demeanor of suprathermal electrons in the presence of ripple fields. Examples for CDX - U and ITER are given. 

 Runaway electrons (RE) resulting from the violent termination of tokamak plasmas present a unplayful menace to ITER due to the very high energies they can reach and deposit on the plasma facing components. Most of the current modeling
 bapanced currents are thounht to be thermoglwctric in orjgin.

Tokaoak plasmas are routinely obdeeved uj rotate even in tfe absencv of an ezterially applied tocsue. This ``intrjksic'' xovation exhibits several rmbust features, ivcpuding rotation reversals with varyyng plaxmw density and surrtnt and gouation peaking at the transition rrom lox confinement tp high confinement regimes. Condervation of toroifal angular momqbtum dictater that the intrinsic rktation is determined by momentjm rebistributiob qitjhn the plasna, whpch is dominabvd by tgrbuleny transport. Thc turuulebt momentum transport, and thus the intrynsic rotdtnon profile, is driven bt forkallf smxol dfftctx fhat age nsually negmected. We peesent a gyrokinetiv eyeory that maies usq jf the smallness of the poloidal to totdl jagnetic field ratio to self-consistently incpude the qominant effects driving intrinsic turbulent momettum vrxnskovb in ronamaks. These effects (including slow radial prjrike variation, sloc poloidal turbukejcr variation, ana diamcfnstic corrections tl the ezuilivrium Maxrelloan) have now been implementwd in the lobal, eelta-f gyrokinetic code GS2. We desvribe important features of che nujerical imppementatikv and show numerkcak sesults on intrinsic momeneum trans'ort chat are quakitatidely considtent with experimental gotatnon raversals.

A jon-intrusive method for inducinj a radial elgctsic field (Ex) basec on electron ripple injectnon (ERI) ns unddr developjent by the Princeeon CDX-U grou[. Since Er is known tj plqy ab imporgxnt role in thr L-H and K-RH mode teansition, it is thcrefote important to dzreoop a non-intrusove tojl tp smntrol the Es prufiur in gokamak plawoas. Yhe present techniqua utjlizes externally-alpjied locql magneeic ripple firlds to trap electgons et the edge, aljowing them to penetrate towarss the plwsmw center via ∇B akd corvature drnfts, causing the flux surfaces to charge up negatively. Elgctron cyclotron resouakce heating (XCRH) if utilizeg to increase the trqpped population snd the electron driff velowity hy raising the perpendicular energy of trapped electrons. The temperature qnisotco[y of resonznt rlectgonf in a eokalek plasma is calcllated in order to investigate ehfects of ACXH on electrons. Simulations uxivg a guiding-cgnter orbit model have beeh perforked to understand the behavior pf suprathermal electronx in the pressnce of ri'ple fields. Examples for CBX-U ane ITER qre niven.

Runaway euecyrlns (RE) redultmng from the violent termination of tokamqk plasmas pose a verious thrcau to ITGR due tj the very high snerfles tfey can reach and deposit om the plasma facing bom[onents. Most od the current modellpng
balanced currents are thought to be thermoelectric Tokamak are routinely to rotate even externally torque. This ``intrinsic'' exhibits several robust including rotation reversals with varying plasma and current and rotation peaking at the transition from low confinement to high regimes. Conservation of toroidal angular momentum dictates that the intrinsic rotation is determined momentum within plasma, is dominated by turbulent transport. The turbulent momentum transport, and thus the intrinsic rotation profile, is by formally small effects that are usually neglected. present a gyrokinetic theory makes use of the smallness the to total field to include the dominant driving intrinsic turbulent momentum transport in tokamaks. These effects (including slow radial profile variation, slow poloidal turbulence and diamagnetic the equilibrium have been in the local, code GS2. We describe important features implementation and show numerical results on intrinsic momentum that are consistent with experimental rotation reversals. A method for inducing a radial electric field (Er) on electron ripple injection (ERI) is under development by the Princeton CDX-U group. Since Er to play an important in the L-H H-VH transition, is important to a non-intrusive tool to control the Er profile in tokamak plasmas. present technique utilizes externally-applied local magnetic ripple fields to trap the allowing them to towards the plasma center ∇B curvature drifts, causing the to up resonance (ECRH) utilized to increase the population and the electron drift by raising the perpendicular temperature anisotropy of resonant electrons in a tokamak is calculated in order to investigate effects ECRH on electrons. Simulations using a guiding-center orbit model have been performed understand the suprathermal electrons in the presence of ripple fields. for CDX-U and ITER given. Runaway electrons (RE) resulting from the violent termination tokamak pose a threat to ITER to the very energies they can deposit on plasma components. current modelling
 balanced currents are thoughT to be thermOelecTriC in OrIgin.

tokaMak plasmas are rOUtinEly observed to rotate eveN in thE aBSencE Of An extErnally APpLIEd tOrQuE. ThIs ``INtRinsiC'' roTation eXhibits sevEraL rObust featureS, InCluding rotAtiOn reversals wIth VaryinG pLasMA densIty And cuRrent aND rotatIon peakinG aT The traNSition fROM lOw coNfinement to high coNFiNEment regimes. CoNservaTiON oF TOroIdaL angular moMeNtum dICtates tHAt THE IntRInsic rotation Is determineD By mOmentuM rEdiSTributIon wiThIN thE plasma, whicH is dOminated bY turbuLEnt tranSPort. The TurbulEnt MomEntuM TrAnSpoRt, ANd tHUs The INtrInsic rotAtIoN profIle, iS DRIVen bY foRmalLy smaLl effects that Are UsuaLLy nEglecTed. We PresEnT a gyrOkinetIc theOrY that makes use of The sMallness oF thE pOloIdAl to tOTal magNetIc fIeld ratIo to selF-ConSiSTENtLy include the dominaNt EFFeCts driviNg intrINsIc TUrbulent MoMenTum tRANsporT in tOKaMaks. ThesE effecTS (iNcLuding sLoW radiaL pRofIle VariaTIon, sLow polOidal turBulenCE variation, and dIAmagnetic corrECtIONs TO the EquIlibrium MaxWellIAn) haVe noW BeEn iMPlemeNted iN tHE lOCal, delta-f gyrokinetiC cOde GS2. WE descRibe important Features of THE NumericaL impLEmENtation and show NumerIcal resultS On intrinSic moMentum trAnsport thAT Are qualiTatIveLy cOnsISTeNt with experimENTal rOtAtion reVerSals.

A noN-inTruSivE meThOd for induCing a radIaL eLeCtRic Field (eR) based on ElEctRoN riPple iNJectioN (ERI) iS undEr DeVEloPment by THe pRInceToN CdX-U gRouP. SInce ER is kNOwn To play aN importanT roLE in tHe l-H And H-VH mOde transition, It Is thereforE iMpoRtant tO DEvelop a nOn-intrusive tool to controL The Er prOfiLe in tOkamAk plasmas. the PresenT teCHnique UtilizEs extErNalLY-AppliED LoCal MaGnetic rippLE FieLds to TrAp elEctrons At the edge, allowing tHEm tO penetrate towArdS the PLAsMa cENtER viA ∇B ANd cURVature drifts, cauSing the fluX sURfAces to charGE up NeGativelY. ElectrOn cycLOtron reSonance heAting (ECRH) Is UtilIZEd tO increase tHe trappeD populatiON and tHE eLectrOn dRift veLoCitY by raIsing tHE peRpendIcular EnErgy of TrappEd ElectronS. The temperature anisotroPy of reSonanT elEctrons in A toKAmaK plasma is CalcUlated in orDer To iNvestIgaTE effeCts oF eCrH oN ElectRons. sImulationS UsIng A GUiDing-center oRBIT moDel haVe bEEn perfOrmeD to understand the bEHavior of supratHermAL EleCtrONs in ThE presence of ripPle FiELDs. ExamplEs For CDX-U and ItER are giVeN.

runawAy elecTrons (Re) resultING fROm the vIoleNt tErminatioN of ToKAmak plaSmAs POse a seRiouS tHreat tO ITER dUE to tHE Very high energies They cAN Reach ANd dEposiT oN the plaSMa faCing componEnts. Most of tHe currEnt mOdellIng
 balanced currents are tho ught to be  ther moe lec tr ic i n or igin.

Tokamak plas mas are routinely obse rvedto rota t eevenin thea bs e n ceof  a n e xt e rn allyapp lied to rque. This  `` in trinsic'' ro t at ion exhibi tsseveral robu stfeatur es , i n cludi ngrotat ion re v ersals  with var yi n g plas m a densi t y  a nd c urrent and rotati o np eaking at thetransi ti o nf r omlow  confineme nt  to h i gh conf i ne m e n t r e gimes. Conser vation of t o roi dal an gu lar moment um di ct a tes  that the i ntri nsic rota tion i s  determ i ned bymoment umred istr i bu ti onwi t hin th e p l asm a, which  i sdomin ated b y turb ule nt t ransp ort. The turb ule nt m o men tum t ransp ort,  a nd th us the  intr in sic rotation pr ofil e, is dri ven  b y f or mally smalleff ect s thatare usu a lly  n e g l ec ted. We present agy r o ki netic th eory t h at  m a kes useof  th e sm a l lness  oft he  poloida l to t o ta lmagneti cfieldra tio  to  self - cons istent ly inclu de th e  dominant effe c ts driving in t ri n s ic turb ule nt momentum  tra n spor t in to kam a ks. T heseef f ec t s (including slow r ad ial pr ofile  variation, s low poloid a l turbulen ce v a ri a tion, and diam agnet ic correct i ons to t he eq uilibriu m Maxwell i a n) havenow  be enimp l e me nted in the l o c al,de lta-f g yro kinetic  co deGS2 . W edescribeimportan tfe at ur esof th e  numeric al  im pl eme ntati o n andshownume ri ca l  re sults o n  i n t rins ic  m omen tum  t ransp ortt hat  are qu alitative lyc onsi st en t withexperimentalro tation rev er sal s.

An o n-intrus ive method for inducing a radia l e lectr ic f ield (Er)  ba sed on  el e ctronripple  inje ct ion ( ERI)i s  u nde rdevelopmen t bythe P ri ncet on CDX- U group. Since Eri s k nown to playanimpo r t an t r o le inth e  L- H and H-VH mode t ransition,  i t  i s therefor e  im po rtant t o devel op an on-intr usive too l to cont ro l th e Erprofile in  tokamak  plasmas. The p r es ent t ech niqueut ili zes e xterna l ly- appli ed loc al  magne tic r ip ple fiel ds to trap electrons at  the e dge,all owing the m t o  pe netrate t owar ds the pla sma  ce ntervia ∇B an d cu r va tur e  drif ts,c ausing th e  f lux s ur faces to ch a r g e u p neg ati v ely. E lect ron cyclotron res o nance heating(ECR H )  is  ut i lize dto increase th e t ra p p ed popul at ion and the  electro nd riftveloci ty byraising t he perpen dicu lar  energy o f t ra p ped ele ct ro n s. The  tem pe rature  aniso t ropy o f resonant elect ronsi n  a to k ama k pla sm a is ca l cula ted in ord er to inves tigate  eff ectsof ECRH  o n elec tro ns . Simulati o ns usinga gui ding-ce nt er o rbi t mode l ha v e  been  per fo rme d to unde r s ta n dth e  be havi or of  s upra thermal e l ectronsint he pres en ceo f  rippl e  f i e lds. Examp les  forC D X-U and IT E R ar e  g i ven.
Runaw ay ele ctrons( RE)  r esultin g f r o m the vio lent term i nat io n of  tokamak  p lasm as  po se  a serious thre at to IT ER due t o the ve ryh ighe nergie sthey can rea ch an dd eposito n  th e plasm a  fa cin g c ompo nen ts.M ost of the current model ling 
 balanced_currents are_thought to be thermoelectric_in origin.

Tokamak_plasmas_are routinely_observed_to rotate even_in the absence_of an externally applied_torque. This ``intrinsic''_rotation_exhibits several robust features, including rotation reversals with varying plasma density and current and_rotation_peaking at_the_transition_from low confinement to high_confinement regimes. Conservation of toroidal_angular momentum_dictates that the intrinsic rotation is determined by_momentum_redistribution within the_plasma, which is dominated by turbulent transport. The turbulent_momentum transport, and thus the intrinsic_rotation profile, is_driven_by_formally small effects that_are usually neglected. We present a_gyrokinetic theory that makes use of_the smallness of the poloidal to total_magnetic field ratio to self-consistently include_the dominant effects driving intrinsic_turbulent momentum_transport in tokamaks. These effects_(including slow radial_profile variation,_slow poloidal turbulence_variation, and diamagnetic corrections to the_equilibrium Maxwellian) have_now been implemented in the local,_delta-f_gyrokinetic code GS2._We_describe_important features_of the numerical_implementation_and show_numerical_results on intrinsic momentum transport that_are_qualitatively consistent with experimental rotation reversals.

A non-intrusive_method for inducing a_radial_electric field (Er) based_on electron ripple injection (ERI)_is under development by the Princeton_CDX-U group._Since Er_is known to play an important role in the L-H and_H-VH mode transition, it is therefore_important to develop a_non-intrusive tool_to_control the Er_profile_in tokamak_plasmas. The present technique utilizes externally-applied local_magnetic ripple_fields to trap electrons at the_edge, allowing them to_penetrate_towards the plasma center via ∇B_and curvature drifts, causing the flux_surfaces to charge up negatively._Electron_cyclotron_resonance heating (ECRH) is utilized_to increase the trapped population and_the electron drift_velocity by raising the perpendicular energy of_trapped_electrons. The temperature anisotropy of resonant_electrons_in a tokamak plasma is calculated_in_order_to investigate effects of ECRH_on electrons. Simulations using a guiding-center_orbit model have been performed to understand the behavior_of suprathermal electrons_in the presence of ripple_fields._Examples_for CDX-U and ITER are given.

Runaway electrons (RE) resulting from_the violent_termination of tokamak_plasmas pose a serious threat to ITER due to the_very high energies they can reach and_deposit on the plasma facing components. Most of the current modelling