The hard X-ray intensity radial profiles from lower hybrid current drive experiments are interpreted as being correlated with fluctuations in the bulk plasma. This view seems to be dictated by comparing the hard X-ray data for various n║ with the Monte Carlo solutions of the lower hybrid wave energy deposition on plasma electrons. Information on internal magnetic fluctuations may, under certain conditions, be unfolded from a n║ scan of the hard X-ray profiles

Bonoli, Paul T.

Vahala, George

Vahala, Linda L.

English

Old Dominion University

Old Dominion UniversityODU Digital CommonsElectrical & Computer Engineering FacultyPublications Electrical & Computer Engineering1992Effect of Fluctuations on Lower Hybrid PowerDeposition and Hard X-Ray DetectionGeorge VahalaLinda L. VahalaOld Dominion University, lvahala@odu.eduPaul T. BonoliFollow this and additional works at: https://digitalcommons.odu.edu/ece_fac_pubsPart of the Electrical and Computer Engineering Commons, and the Plasma and Beam PhysicsCommonsThis Article is brought to you for free and open access by the Electrical & Computer Engineering at ODU Digital Commons. It has been accepted forinclusion in Electrical & Computer Engineering Faculty Publications by an authorized administrator of ODU Digital Commons. For more information,please contact digitalcommons@odu.edu.Repository CitationVahala, George; Vahala, Linda L.; and Bonoli, Paul T., "Effect of Fluctuations on Lower Hybrid Power Deposition and Hard X-RayDetection" (1992). Electrical & Computer Engineering Faculty Publications. 35.https://digitalcommons.odu.edu/ece_fac_pubs/35Original Publication CitationVahala, G., Vahala, L., & Bonoli, P.T. (1992). Effect of fluctuations on lower hybrid power deposition and hard x-ray-detection. Reviewof Scientific Instruments, 63(10), 4682-4684. doi: 10.1063/1.1143662Effect of fluctuations on lower hybrid power deposition and hard x-ray detection George Vahala Department of Physics, College of William & Mary, Williamsburg, Virginia 23185 Linda Vahala Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, Virginia 23529 Paul T. Bonoli Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (Presented on 16 Marfch 1992) The hard x-ray intensity radial profiles from lower hybrid current drive experiments are interpreted as being correlated with fluctuations in the bulk plasma. This view seems to be dictated by comparing the hard x-ray data for various ~11 with the Monte Carlo solutions of the lower hybrid wave energy deposition on plasma electrons. Information on internal magnetic fluctuations may, under certain conditions, be unfolded from a nl( scan of the hard x-ray profiles. I. INTRODUCTION In recent years, lower hybrid (LH) waves have been utilized for electron and ion heating, to sustain and rampup the toroidal plasma current, and to stabilize saw- teeth instabilities.* An accurate prediction of the lower hy- brid current drive (LHCD) profile is important in assess- ing the feasability of each of these applications. Thus, it is of interest to ascertain the effects of wave scattering from both density and magnetic fluctuations on the propagation and absorption of LH waves. Typically, computer models’ of LH heating and current drive concentrate on the con- finement properties of the suprathermal tail electrons pro- duced by LHCD and the transport properties of the back- ground electrons. In these models, a one-dimensional ( 1D) radial transport code is coupled to a Fokker-Planck toroi- dal ray tracing code. While it is known that density fluc- tuations2 can play a major role on LH wave propagation, it is computationally prohibitive to incorporate these scatter- ing effects into the transport LHCD simulation model. Here, we explicitly examine the effects of fluctuations on LHCD, and connect these wave scattering results to hard x-ray emission3 caused by collisions of the suprather- ma1 electrons with the background plasma ions. In partic- ular, the results from a Monte Carlo solution of a wave kinetic equation that now includes both density and mag- netic fluctuations are compared with hard x-ray intensity radial profile measurements4 from JT-60. We then consider Alcator C-Mod parameters and find that an analysis of experimental radial hard x-ray intensity profiles could dis- tinguish between magnetic and density fluctuation scatter- ing provided the fluctuation levels are sufficiently high. Thus, this hard x-ray diagnostic (a standard diagnostic on LHCD experiments) could then be combined with a re- cently proposed microwave mode-conversion scattering scheme’ to assess the level of internal magnetic fluctuations in a tokamak. The determination of magnetic fluctuation levels and structure has strong implications on general plasma transport. II. WAVE KINETIC EQUATION FOR DENSITY AND MAGNETIC FLUCTUATIONS The theory of Bonoli and Ott2 for LH wave scattering from density fluctuations is extended to also include the effects of magnetic fluctuations. Using weak turbulence theory, one finds that the wave energy density F is deter- mined by ,+2y(x,k)F(x,k,t) = s m c~K~(K-K,)~; dP[F($+P) --F(P) I 0 x tS%) 1 v(k$G/3) I” +S$dK) [V:(‘b,K,b) $(k, ,K,D) 12]. (1) (dF/dt) r is the time evolution of the wave packet following a ray trajectory in a toroidal tokamak equilibrium and y is the wave damping due to resonant electron and ion Landau damping as well as collisional damping. The right- hand side of Eq. (1) gives the effect of fluctuations on the ray trajectory. The fluctuations scatter the wave number kl through an angle /3 to a new wave number k; , with k,*kl=k,k;cos@ and K=(kl-k{l. v” and VB are the density and magnetic coupling coefficients, while 5”’ and the tensor SB are the corresponding wave number fluctua- tion spectra. Equation ( 1) is solved by a Monte Carlo procedure.’ For the results presented here, each electron radial power deposition profile is averaged over 100 runs, It should be noted that the parallel wave number k,( varies because of magnetic shear, toroidicity as well as by the scattering process itself. These changes to k,, directly effect the accessibility of the LH wave (nll=ck,l /o > n,) as well as the strength of the electron damping [n/I <n,I,,-7,0/ Ti’2(keV)] of the LH wave. 4662 Rev. Sci. Instrum. 63 (lo), October 1992 0034-6748/92/104682-03602.00 @  1992 American Institute of Physics 4682  Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions.  IP:  128.82.253.131 On: Mon, 15 Feb 201615:34:24Hard X-Ray lnrensity (a.u) 1.2 1 0.8 033 0.4 ; 0.1/i ; ; “f;;;;--;\ 0 0.2 0.4 0.6 0.8 I r/a FIG. 1. Radial profile of the hard x-ray diagnostics with four channels on JT-60 (Ref. 4). III. ELECTRON POWER DEPOSITION AND HARD X RAYS We first consider the JT-60 tokamak for which the radial profiles for the hard x-ray signals are given for var- ious nil at three radial chord positions,4 Fig. 1. For these JT-60 parameters (u = 93 cm, &,= 300 cm, r,= 2-3 keV, Bo=4T, Itor= 1 MA, neo= 1.5X lOI cmm3 and LH wave frequencyfo=2 GHz) we show in Fig. 2 the Monte Carlo results for the radial electron power deposition profiles for a density fluctuation level (&z/n,)*= l%, peaked at the plasma edge [the “pe-n” curves]. Two magnetic fluctuation spectra are considered on top of these density fluctuations: the “pe-m” curves for which the magnetic spectrum is also peaked at the plasma edge, and the “pe-mm” curves for which the magnetic spectrum is peaked internally at r/a =0.6. The level of magnetic to density fluctuations is as- sumed to be5 w: )/& 1 1 (&2)/n~ peak= 10-4. (2) Also shown in Fig. 2 is the electron power deposition if there were no fluctuations (density or magnetic) present [“pe-vat”]. One immediately sees a strong similarity be- tween the structure of the hard x-ray profiles and the elec- tron power deposition profiles provided fluctuations are taken into account. Clearly, if one ignores the effects of fluctuations, the corresponding power deposition profiles are markedly different from those coming from the exper- imental hard x-ray profiles. Although fast electrons can diffuse spatially before they thermalize (so that the rf power deposition profiles may not exactly track the t-f cur- rent density profiles), we feel that the hard x-ray profiles are directly correlated to the presence of fluctuations in the plasma. It is apparent from Fig. 2 that for JT-60 it is not expected to be possible to distinguish density from mag- netic fluctuations in the hard x-ray diagnostics. Moreover, the Monte Carlo solutions of Eq ( 1) indicate that this 0.05 0 ..*.I-+?-” -pe-m ---pe-mm r/a (al 0 0.2 0.4 0.6 0.8 1 electron power JT-60 0.4 1% flwt lev& I+ = 1.93 0.35 0.3 0.25 ;; ,* :; ! : 4  I : : I I I I I I I : : t -----pe-vat ..,.p+” -pe-lTl ---pe-mm (b) 0 0.2 0.4 0.6 0.8 1 JT-fxJ[e=o”l elech-on power 1% fluct., I+ = 2.88 -----pe-vat ..e.peq --plYll ---pe-mm 0 0.2 0.4 0.6 0.8 1 (c) FIG. 2. Electron power deposition profile for JT-60 in the divertor mode [edge density fluctuation level =: l%] for various n,i. pe-vat: no fluctua- tions, pen: only edge density fluctuations, pe-m: edge density and mag- netic fluctuations, pe-mm: edge density fluctuations and internal magnetic fluctuations. (a) nl,=1.3, (b) n,, =1.93, (c) q=2.88. The fluctuation deposition profiles seem to track the experimental hard x-ray data of Fig. 1. 4683 Rev. Sci. Instrum., Vol. 63, No. 10, October 1992 Plasma diagnostics 4683  Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions.  IP:  128.82.253.131 On: Mon, 15 Feb 201615:34:24Alcztm CMod[e-27001 elecuon power 10?6lkct,rj=2.0 ;; 4 .0.105 I i i --o-p?!-Ill I t : I - - -pe-mm : : 0 0.2 0.4 0.6 0.8 1 (a) AlatorCMcd[B=27~ electron power 10?6fllk& I$=25 0.25 -----pe-vat ..,.p+” -p+m - - -pe-mm 0.05 0 0 0.2 0.4 0.6 0.8 I (b) FIG. 3. Electron power deposition profile for Alcator C-Mod parameters ’ P. T. Bonoli, AIP Conf. Proc. 159, 85 ( 1987). in the limiter mode [edge density fluctuations =. lo%] for (a) rr,,=2.0, ‘P. T. Bonoli and E. Ott, Phys. Fluids 25, 359 ( 1982). and (b) tz,I=2.5. Since it seems that the fluctuation power depositions ‘S. Texter er al., Nucl. Fusion 26, 1279 (1986). determine the hard x-ray diagnostics, then it should be able to decem 4K. Uehara er a6., AIP Conf. Proc. 190, 106 (1989). internal magnetic fluctuations from hard x-ray intensity profile scans in *L. Vahala, G. Vahala, and N. Bretz, Rev. Sci. Instrum. 61, 3022 91 . (1990); Phys. Fluids B 4, 619 (1992). 4684 Rev. Sci. Instrum., Vol. 63, No. 10, October 1992 Plasma diagnostics statistical similarity in the three fluctuation spectra (pen, pe-m, pe-mm) persists even if JT-60 is run in a limiter mode with a resultant edge density fluctuation levels of 10%. In Fig. 3, the electron power deposition profiles are shown for Alcator C-Mod [a = 2 1 cm, R. = 67 cm, T& = 5 keV, Bo= 9 T, I,,,= 3 MA, n,,=3.5X1014 cmw3, and fc =4.6 GHz] run in a limiter mode, with a peak edge density fluctuation level of 10%. For nlt=2.0, Fig. 2(a), there is substantial statistical difference between the power deposi- tion curves for pen and pe-mm over that for pe-m, the case of both density and magnetic fluctuations peaked at the edge. For nll=2.5, there is now a substantial difference between electron power deposition for magnetic fluctua- tions peaked internally (pe-mm) over magnetic fluctua- tions peaked at the plasma edge ( pe-m), or the case of only density fluctuations (pe-n), Fig. 2 (b) . LH waves drive suprathermal electrons, and it is the prompt collisions of these suprathermal electrons with the background plasma that gives rise to the hard x rays.3 We thus expect that these power deposition differences should be reflected in a hard x-ray intensity radial nil scan and so give important information on the fluctuations within the plasma. If so, then hard x-ray data, together with the di- agnostic results from the proposed microwave scattering for the detection of internal magnetic fluctuations for Al- cator C-Mod, should give more insight into the correlation between internal magnetic fluctuations and bulk plasma transport. ACKNOWLEDGMENTS This work was supported by Department of Energy grants to William & Mary, O ld Dominion University and Massachusetts Institute of Technology (MIT). 4684  Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions.  IP:  128.82.253.131 On: Mon, 15 Feb 201615:34:24

Effect of Fluctuations on Lower Hybrid Power Deposition and Hard X-Ray Detection

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Effect of Fluctuations on Lower Hybrid Power Deposition and Hard X-Ray Detection

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