Resonant scattering of Lyman alpha radiation as a neutral density diagnostic for fusion plasmas

RESONANT SCATTERING OF LYMAN ALPHA RADIATION AS A NEUTRAL DENSITY DIAGNOSTIC FOR FUSION PLASMAS DAVID W.

KOOPMAN. THOMAS J. MCILRATH and VALERIE P. MYERSCOUGH*

Institute for Physical Science and Technology. University MD 20742. U.S.A.

of Maryland. College Park.

Abatract-Resonance fluorescence of neutral hydrogen illuminated by Lyman alpha radiation (1216 A) provides a technique for spatially and temporally resolved density measurements of neutral hydrogen isotopes in magnetically confined fusion plasmas or other similar environmenls. An analysis of the magnitudeof expected fluorescence signals and intqgraled background radiation is developed and applied to typical fusion plasmas. Assuming that intense Lyman alpha sources. based on nonlinear laser frequency mixing techniques. are available. the feasibility of the method is demonstrated for neutral densities as low as a few times 10’ cm-’ in DITE. PLT and TFTR. Suggestions are made for spectroscopic measurements on current and future Tokamak devices. lo obtain additional data of interest for this application.

I. INTRODUCTION

resolved measurements of neutral hydrogen densities in fusion research plasmas would yield directly data which are currently inferred from spatially averaged techniques such as emission spectroscopy or neatral particle analysis!” Such data would clarify considerably the important role of neutrals in energy and particle loss from fusion plasmas,‘*’in recycling of hydrogen isotopes between plasma and vacuum walls,‘3’and in the operation of divertors, neutral beam injectors and other fuel handling components of a fusion reactor system. In order to obtain accurate measurements of neutral hydrogen-density profiles in highteniperature, low-density plasmas, it is necessary to develop techniques which have good spatial and temporal resolution combined with sufficiently high sensitivity (in order to detect low values of the neutral density) and reasonably simple interpretations. These requirements indicate that laser-induced fluorescence is a suitable diagnostic technique. However, the use of intense dye lasers tuned to visible transitions (e.g. Ha) will not be satisfactory since so few neutrals exist in excited states compared to the number in the ground state: moreover, the results will be difficult to interpret. The technique of laser-induced fluorescence at the wavelength of the resonance transition, Lya. of neutral hydrogen or its isotopes, has been recognized by BRE~ONand PAPOULAR’~‘~and KOOPMANand MCILRATH@’ as a method of obtaining accurate spatially and temporally resolved neutral density measurements with a high degree of sensitivity. An intense beam of Lya (I216 A) radiation would be directed through the region of the plasma ‘to be probed, exciting some of the ground state atoms to the first excited state; subsequent spontaneous re-emission would be detected at an angle to the incident beam. The amplitude of such a scattered signal is directly related to the neutral density in the scattering region. Breton and Papoular had proposed that the U.V. emission continuum from a laser-produced plasma could provide the probing flux. However, McIlrath and Koopman recognized that the frequency-summing techniques developed by MILES and HARRIS”’and used to generate U.V. radiation in the IooO-2000A range(‘) could provide a Lya source vastly brighter than that attainable with any thermal source such as a laser spark or electrical discharge. Preliminary estimates by KOOPMAN. MCILRNH and MYERXOUGH’~-‘~’ indicate that a coherent source of radiation at 1216 A, based on frequency tripling of radiation at 3648 8, in a phase matched gas mixture, could generate collimated probing radiation at a power level P between 10 and 100kW within the Lya Doppler profile, for a duration of 5-10 nsec. The 3648 A radiation could be obtained, for example by SPATIALLY

tpermanent England.

address: Department

of Applied

Mathematics.

555

Queen Mary College.

University

of London El 4NS.

556

D.W.K~OPMANrf (I/.

frequency doubling the output of a tunable dye laser at 72%A using conventional nonlinear crystals. Such a source would provide a far higher degree of sensitivity than that attainable using the U.V.continuum from a laser-produced plasma, which generates only a few watts of collimated radiation within the Lya Doppler profile. This paper examines the applicability of such a source to large Tokamak devices. A detailed theoretical model for resonant optical excitation of neutral hydrogen in a plasma is developed in Section 2. In Section 3, relevant signal amplitudes and signal to noise estimates are considered: these results are used to demonstrate the feasibility of neutral scattering in the DITE, PLT and TFTR devices in Section 4. The paper concludes with a discussion of the results and suggestions for further experimental investigations. 2. COLLISIONAL-RADIATIVE

ANALYSIS

OF HYDROGEN

In order to interpret Lya fluorescent scattering, the local atomic state populations for neutral hydrogen in a plasma environment before and during illumination by a Lya source must be obtained. For the conditions typical in Tokamaks and other magnetically confined plasmas, a multi-level, time-dependent, collisional-radiative model has been developed assuming an optically thin hydrogen (e-H’-H) or hydrogen isotope plasma. The electron temperature T,, electron density n, and neutral hydrogen density NH are functions of radial position r measured from the center of the plasma, but vary only on time scales of a few tens of milliseconds during the steady plasma discharge. The rate equations for the local atomic populations Ni of the ith level of neutral hydrogen in the absence of the external radiation source [MCWHIRTER and HEARN.(“) JOHNSON and HINNOV.“” KOOPMAN et a1.““]

can then be written

as

n’

+

Yj)+6i,@* j=z+, NT(neXj;+ Aji) + n,Z(cU;+

(ISiSn),

(2.1)

where X;j and Xi; (cm’ set-‘) are the collisional transfer rates between state i and other discrete states, Xi, Yi(cm3set-‘) are, respectively, the collisional ionization and recombination rates, aj(cm3sec-‘) is the radiative recombination rate, and AJj > i)(sec-‘) is the spontaneous emission rate. We used JOHNSON’S”~’ analytic expressions for the rates; these are essentially exact for Aji and ai and should be very accurate for the electron collision rates at high temperatures since the Maxwellian velocity distribution peaks close to the Born region of the cross sections. The assumption that the plasma is optically thin in the Lyman lines is valid in present day Tokamak plasmas provided the neutral density is less than about IO” cmV3. The 1 and mf sublevels of the ith level are assumed to be statistically populated (primarily by proton collisions) which requires an ion density greater than about lOI cm-3.04’Also, we have included a net rate @ of influx (by diffusion or resonance charge exchange) of ground state neutrals.“” Strictly, eqns (2.1) form an infinite coupled set. However, for sufficiently large values of n, the levels j> n are strongly coupled by collisions to each other and to the continuum. Thus, these levels are in LTE with the continuum and have populations Nf given by the SahaBoltzman equation and achieved on extremely short time scales (much less than 1 nsec); typically n lies between 8 and 13. The effect of these high levels can then be included in the rate equations for 1 d i c n by summing the appropriate terms to n’, where n’ is chosen on convergence criteria and lies typically between 20 and 25. In order to study the time dependence of the local level populations, eqns (2.1) may be expressed in matrix form for given T,, n, (which are considered as constants over time scales short compared to those for evolution of the plasma) as $+AN=B.

(2.2)

where N is the (n x I) column vector of level populations Ni, A is the (n x n) matrix of coupling

Resonant scattering of lyman alpha radiation

551

coefficients and B is the (n x 1) column vector of recombination terms. The matrix A is nonsingular and nonsymmetric but possesses real, distinct and positive eigenvalues Ai,(1 d i s n). Consequently the solution of eqn (2.2) is both stable and asymptotically stable and may be written as N = Q e-A’Q-‘[N,,o- A-‘B] + A-‘B,

(2.3)

where Q is the matrix of eigenvectors of A, A is the (diagonal) matrix of eigenvalues of A, and NIEois the initial value of N, which is specified as the total neutral density NH with all the atoms assumed to be in the ground state. The level populations are then given by

Ni=$Wiie-*]'+(A-'B)i

l
(2.4)

i=l

where the coefficients wii may be obtained from eqn (2.3). The local level populations given by eqn (2.4) have been calculated for a wide range of the parameters n,(r), T,(r) and NH(~) typical of Tokamak and other plasma regimes. For the values of T, and n, considered, this formulation leads to matrix A whose smallest eigenvalue is many orders of magnitude less than the next few, which are typically about 10’ (set-‘). Consequently, after a few tens of nanoseconds, the local populations given by eqns (2.4) achieve quasi-steady values. Physically, the populations of the levels i 2 2 reach equilibrium with respect to the ground state and the continuum, but the ground state population is effectively unaltered from its original value. NH, given by diffusion and resonance charge exchange. This quasi-steady state corresponds precisely to the situation analyzed by MCWHIRTER and HEARN”” and JOHNSON and HINNOV””and, using Johnson’s rates,‘13’ we reproduce exactly the quasi-steady populations obtained from JOHNX’N and HINNOV.“”Moreover, for the estimates of n,, 7’, and NH in present Tokamak plasmas, the quasi-steady population N,’ of the first excited state is proportional to NH where the proportionality factor depends on np and T, and is given approximately by the coronal result

K”(r) _ n,(r) . WTh9l NH(r)

Q

1

(2.5)

~421

Having obtained the local quasi-steady populations N/, the effect of irradiation of a small volume element by a collimated pulse F kW/cm’ of Lya radiation having a full width 2Av,(Hz) and a time duration TL(set) must be considered. For simplicity, a pulse square in frequency and time is assumed; simple modifications can be made for actual experimental pulse shapes. Equations (2.1) then contain the additional terms - NlRi2+ N2R2, and NlR12- N2R2, in the expressions for dN’/dt and dNz/dt, where R’z and R2’ (set-‘) are, respectively, the photoexcitation and stimulated emission rates induced.‘by the source; at the power levels anticipated, photoionization of levels i 3 2 is negligible compared to other competing processes. For the plasma conditions prevalent in a Tokamak discharge, the Lya line is broadened almost entirely by the thermal motions of the atoms, so that the line shape is approximately Gaussian with a l/e half width given by AvD= (~‘~/c)(2kTIM)~‘~Zfz,where T is the local neutral temperature in “K and M is the mass of the neutral hydrogen isotope. With a half width AuL greater than I.5 AvD, the source irradiates almost all of the Lya line and R,2

=

10°F ?T e2 *--fj2sec hu1262AvL mc

-I

,

(2.6)

where F(kW/cm’) is the incident power per unit area, hv12(ergs) is the transition energy, and (B e2/mc)f’2 (cm*Hz) is the cross section of the transition integrated over the line profile. Rzl is related to RI2 through statistical balance, Rz’ = (g’/g~)R’~, where the degeneracies here are g, = 2, g2 = 8. The local populations in the presence of an irradiating Lya source may now be obtained in the form of eqn (2.4), using the modified eqns (2.1) and taking as initial conditions the

D.W. KOOPMAN et N/

558

corresponding local quasi-steady populations N/’ prior to the onset of the pulse. For the anticipated values of the source power per unit area, F. a new quasi-steady state is achieved on a time scale comparable to or shorter than the spontaneous lifetime of the first excited state, that is. in one or two nanoseconds. The resulting quasi-steady population NzF is again proportional to Nn, the proportionality factor now depending on rrp, T, and E”” After detailed calculations of numerous cases which model Lya illumination of a Tokamak plasma environment, we conclude that a good approximantion for the population of the first excited state during illumination byLycY may be obtained by consideration of the equivalent local “coronal” model 2

= N,(n,X,z + Rd - N2(A2, + Rz,),

0.7)

subject to the initial condition (2.5) that N! = Nz” = NH~,XJA~, at t = 0, together with the assumption that NZ+ N, = NZo+ NIo = NH, which implies that little collisional or radiative interaction with other quantum states or the continuum occurs on the short time scales considered. Since, in Tokamak plasmas, rr,X,? Q A 2,. this term may be neglected in comparison to A?,, so that the solution of eqn (2.7) may be expressed in the form

N?(r) -=-__

NTF(r)

NH(r) NH(r)

-A,

ye ’

(2.8)

where A = [I + (g1/g2)1R12 + AZ, set-‘, y = [iV~F(r)/Ndr)l - [Nz”(r)/iVdr)l, and A$’ is the quasisteady value reached after a few nanoseconds in the presence of the Lya source; that is,

u NH(r)

=n,(r) . XdT,(r)]

+ RI2 [I + (g,/gn)lR,z+ AZ, ’

(2.9)

As the value of RI2 is increased, this ratio approaches 0.8 asymtotically, since the levels saturate at radiative equilibrium with Rzl %= A 21.The degree of saturation is appreciable when Rz, = A*,, or NZF(r) = 0.66NH(r), which, for AvL = 1.5Avo, corresponds to values of F reaching F, = 95( TH/MH)“*kW/cm* where TH is the neutral temperature in eV and MH the mass in amu. However. substantial enhancement of the first excited state population occurs for considerably lower values of F. since, for the situation n,X,z < Rzl < A?,, the local quasi-steady population Nzo. given by eqn (2.5). prior to irradiation is substantially less than the value of NZF [given by eqn (2.911 during the laser pulse. Under these conditions, which are likely to be appropriate for the anticipated Lya source powers and central neutral temperatures, the quantity NzF(r)- Nzo(r). which is proportional to NH, is also approximately proportional to F. The results obtained from the analytic“corona1” model (2.7) for the behavior of the population of the first excited state of neutral hydrogen agree very well with those from the full solution of the modified eqns (2.1) over a wide range of T,, n,. NH and source power per unit area, F. Figure 1 shows a comparison before and during a 10 nsec pulse of Lya radiation, for the plasma conditions specified. and illustrates the good agreement between the two models. The rapid rise, from the initial quasi-steady state N,” prior to irradiation to the quasi-steady state NZF during irradiation, is clearly seen, and the decay of the enhanced population at the termination of the pulse with a time constant AZ, is evident. We conclude that eqns (2.5) and (2.8) are a satisfactory approximation to the first excited state population densities expected in applying Lya fluorescence techniques to Tokamak plasmas, and we shall use these results in the next section to estimate the anticipated sensitivity of such an experiment. However, the full multi-level treatment is required to study the effect of collisionally-induced fluorescence for higher levels due to irradiation by the Lya source(‘“’ or to analyze more complex situations such as optical probing at other transition wavelengths. Further, at very high temperatures. the effect of proton collisions on the populations of levels i 3 3 is significant.“” 3.

SIGNALAMPLITUDESANDBACKGROUNDEMISSION

Figure 2 presents a suggested arrangement of a Lya fluorescence experiment on a typical toroidal or cylindrical plasma. A source L projects a collimated beam of radius rh(cm). power

Resonant scattering of lyman alpha radiation 1.0

I

I

559

I

10 tfnsec) Fig. I. The ratio NJNn for neutral hydrogen in a plasma irradiated with a Lya pulse F kW cm-’ of duration rr. sec. The plasma conditions are: r, = I keV. Tn = 6OeV. II, = 3 x 10” cm-‘. NH = IO” cm-‘. Avl = 1.5 AVO. Mn = I amu. with F = 0 for I
Fig. 2. Suggested arrangement of a Lya fluorescence system installed on a toroidal or cylindrical plasma experiment. The plasma radius is r,,: a lens of radius r, images the scattering volume onto a mask aperture M. behind which a detector D is located. Lya radiation from a source L passes vertically through the plasma and is monitored by P,,,.

P(kw) and duration TL(sec) through the scattering volume, assumed here to be in the geometric center of the plasma, and thence into a beam absorber, A, where it is monitored by a photo-detector, P,,,. For 90” scattering, a lens, W, at right angles to the probing beam, images the scattering volume onto a mask, M, the aperture in which corresponds to the image of the projected scattering volume which has length I (cm) in the plasma interior. The plasma parameters n, T, Nu, etc. are assumed to vary with radial direction r; the radius of the plasma is r&m); the lens W has radius r,(cm) and is assumed to be located a distance rd(cm) from the probing beam. A photo-detector, D, behind the mask, M, responds only to the Lya photons impinging on W, from within the volume and collection angle defined by r,, I, W and M, with efficiency l and time response rJsec). The instantaneous rate of Lya photon arrival at D will be governed by -I S = Az, N~(r)f(r) d V photons set I

(3.1)

where f(r) is the fraction of photons emitted from position r that are collected by the detector

D. W. KOOPMAN CI ul

560

and the integral is taken over the plasma volume. For calculation of the fluorescence signal, the plasma may be taken as spatially homogeneous over the scattering volume V, = wrh21cm3: for this volume, f(r) = Afl/4~7 where AR = (lrr,*/rdz) ster. The detector current due to emission from this volume produced by fluorescence above the normal Lya background is. from eqn (3.1). (3.2)

where e is in coulombs and we have included the factor T&Q*+ rdz)“’ to allow for the time response of the detector, ?d. -Strictly, eqn (3.2) should include the population Nz(0) during the pulse as a function of time: however, the rise time of N?(O) from N?‘(O) to NzF(0) is likely to be faster that the response time of the detector. Further, from eqns (2.5) and (2.9). Zs is proportional to Hu(O) and is closely linear in the source power P(kW) for Fd F,. Provided the field of view of the detector is small enough, the normal Lya emission background from the entire plasma viewed by D may be obtained by observing that a semi-infinite plane of uniform brightness will project the same intensity at the mask regardless of the position of the plane. The contribution from the plasma at r is thus proportional to N,‘(r) and if we consider a plane volume element having thickness dr, the contribution will be dZt,(r) = e~(A2,/4?r)AiW20(r)2rbl dr. Integrating over the plasma volume then yields ‘11

Zb=ee $oAfl

I - ‘,,

N,“(r) dr amp,

where (z = 7r,,/ cm’ is the area of the imaged portion integrated L.va background E, given by

E, = &

_” Nzo(r)Azl dr I ‘8,

of the probing

beam. In terms of the

photons cm-’ sect’ ster-‘.

(3.4)

that is. the number of background Lye photons emitted per unit area per unit solid angle per second from the surface of the plasma, eqn (3.3) may be expressed as Zb = ee aARE,

amp.

(3.5)

where the coronal approximation (2.5) is used to estimate E,. Expressions (3.2) and (3.5) thus give the expected signal Is and background Zh received by the detector. There will be additional radiation produced by the plasma near Lya, namely bremmstrahlung and recombination radiation due to both hydrogen and highly stripped ions. However, within the present estimates, this is not expected to contribute significantly to the total radiation received by the detector in a band pass of a few A near L.va. Since the duration, Q, of the Lya pulse and the detector response time, ?d, will be short compared to the time scale for evolution of the plasma, the temporal relationship between Is and Zh will be as illustrated in Fig. 3 where Is is shown as a relatively small spike superimposed on 1,. The background current Z, appears with two noise components, SZ,, due to perceived shot noise, estimated as SZt,= (eZb/7d)“* amp, and fluctuations AZb,due to varying plasma conditions or instrumental noise, described by AZ,, = 4Zb amp. The signal to noise ratios are then given by SIN = Z,lSZ,, SIF = Z,lAZ,,;

(3.6)

however, the magnitude of 4 and the characteristic frequency at which plasma fluctuations or noise occur are. at present, unknown. For any set of assumed parameters, S/N maximizes for 76 = TV, while S/F maximizes as rd -0. so values of Td = rL are both reasonable and appropriate. Low frequency filtering can, reduce C$ and remove the overall envelope of I,,. provided Z,, remains within the dynamic

561

Resonant scattering of lyman alpha radiation

Fig. 3. Expected form of detector signal as a function of longer. with the overall envelope corresponding to plasma large scale changes in plasma properties or instrumental nanoseconds, with fluctuations 81, representing

time. The time scale of (a) is milliseconds or lifetime and the fluctuations Al,, representing noise. The time scale of tb) is measured in shot noise, and scattered signal 1,.

response of the detector. At low power both SIN and S/F will be closely linear in the Lya source power. Also, if the neutral density NH(r) is increased overall by a factor q, then both Is and lb are increased by the same factor: thus S/F is unaltered while S/N is increased by q”‘, and the results of any calculation of SIN or S/F can be scaled. 4. ESTIMATES

FOR

Lya

FLUORESCENCE

EXPERIMENTS

ON TOKAMAKS

To examine the signal and background levels expected for resonant scattering of Lya in fusion plasmas, it is necessary to make assumptions about the magnitude and radial variation of the plasma parameters n,, T, and NH. Over the expected range of T, the excitation rate X12[T,(r)] is a slowly varying function, and consequently the integrated background Lya emission is more strongly dependent on the behavior of n,(r) and NH(r), both of which have poorly defined values and steep gradients in the region of greatest contribution near the plasma limiter. To present realistic estimates of S/N and S/F, experimental data for n,, T, and NH are used where available, or estimates of NH(r) are obtained by matching model profiles of this quantity with observed values of the background Lya emission. For the signal. f,. a Lya source halfwidth of 1.5 AvD is assumed, with AvD determined by the central neutral temperature TH. Since the lower values of the anticipated Lya source powers P are expected to give a signal Is roughly linear in P, both SIN and S/F would be improved if the relative source halfwidth were narrower since the power would then be concentrated away from the line wings without incurring saturation effects in the line center. Hence, at the lower values of P, the calculations of Is using a source width 1.5 AVDare minimum estimates. Finally, a value of 4 = 0.01, which corresponds to fluctuations in Ib occurring at the 1% level, has been adopted. (a) Divertor injector Tokamak experiment (DZTE)

For the DITE device at Culham, Abel-inverted experimental data for n,(r), estimates of NH(r) from Abel-inverted H, emission, and Thomson scattering data for TJr) over a range of discharge conditions, both with and without the operation of the divertor, are available!“’ The radial profiles are relatively smoothly varying and hence can be matched analytically. Figure 4 presents theoretical fits to the experimental data for an Hz discharge in DITE with plasma current I = 50 ka, at t = 60 msec, without operation of the divertor. Within the anticipated uncertainties, the experimental results agree well with the ‘Gaussian profiles n,(r) = n,(O)exp( - I&?) cmm3,TAr) = T,(O) exp( - KT?) keV, with KE = 0.0045 and KT = 0.0039. The neutral density can be approximated by N”(r) = Nn(OK1+ an exp [- K& - r)]} cm-‘, where cu = [N&)/N”(O)] - 1, KH = 0.264, and r,, = 26 cm. Other experimental profiles obtained in different operating conditions can also be easily approximated to within the uncertainties of the measurements, by combinations of linear, Gaussian, and exponential expressions. Table I presents the anticipated experimental parameters and signal to noise levels for a

D. W. KOOPMAN et u/.

562

Lya fluorescence experiment in three operating configurations of DITE. The profiles for n,(r), T,(r). NH(T)have been fitted [see Fig. 4 for case (i)] to obtain equivalent experimental estimates of the integrated background Lya emission, E,, and hence I,,. Since the central neutral density is relatively high in cases (i) and (ii). both S/N and S/F are substantial even at low powers, while even for case (iii) S/N are S/F very reasonable. In all three cases, the closely linear behavior of S/N and S/F with increasing P is apparent; this can also be seen from the results of Fig. 5. which shows S/N and S/F presented as functions of Lya source power P(kW) for the DlTE configurations

(i) and (iii).

“e

0.01 1

0

I

8

5

IO

I

r

I5

I

20

Fig. 4.

1

25

!------J 20

40

60

80

100

P(kW)

Fig. 5

Fig. 4. Theoretical firs to Abel inverted experimental density data and Thomson scattering temperature data in DITE: (i) I = 50 kA. t = 60 msec. without divertor: Gaussian n,( IO” cm-‘). Gaussian T,(keV), exponential NH(lO” cm-‘). Fig. 5. Anticipated signal to noise levels for a Lya fluorescence experiment on DITE in configuration and (iii) of Table 1, presented as functions of Lya source power P(kW).

(i)

(b) Princeton large torus (PLT)

For PLT, detailed experimental profiles for n,(r), T,(r) and NH(r) under normal operating conditions are not available. However, experimental estimates for the integrated background Lya emission, E,, obtained from the expected ratio of E, to the measured Lyp emission, calibrated against the H, emission are known.“@ For a typical low density Hz discharge .in PLT with current I = 460 kA, at 300 msec, the measured values of the central electron density n,(O) and central temperature T,(O) are about 3 X lOI cmw3 and 1.8 keV respectively, and the integrated background Lya emission is about 4 x 10” photons cm-* set-’ ster-‘, within an experimental uncertainty of perhaps a factor of 2. The electron density and temperature profiles are claimed to be approximately parabolic while the observed Ly/3 (and thus Lya) emission arises from the outer 5-8 cm of the plasma; the expected neutral density varies from about 10’ cma3 in the plasma center to about 10” cm-’ near the limiter. To model the profiles for n,(r) and TJr) in a typical PLT discharge, parabolic distributions are used, with n,(r) = n,(OHl -a&/r,*) and Tc(r) = T,(O)(l - ag*/r,*), where both aE and aT are close to, but very slightly less than. unity; the precise behavior of n, and T, close to the limiter is not known and variations do not effect the results for S/N and S/F significantly. An exponential form of the same type as that used for case (i) of the DITE data for NH is used to estimate SIN and SIF. Figure 6 shows the theoretical profiles chosen for three models of a typical low density Hz discharge PLT. Model (i) is similar to the expected situation in such a discharge, models (ii) and (iii) have substantially lower central neutral densities [similar to those obtained in Monte Carlo

Resonant scattering of lyman alpha radiation

563

Tabk 1. Anticipatedsignal to noisekvck for a Lya tlaorcacence experimenton DITE. Plasma and geometric pikntmetersused: rp= 26.0 cm; hfH= 1.0amu; rb= 0.5 cm; / = 5.0cm; rw= 2.5cm; rd= 40cm; TL= 1o-‘sec;rd = 10-*sec;r=0.1;~=0.01. (i) I * 50 ; t- 6Omsec; without divertor

(ii) I = 50 kA; t - 60 mwc.; with divertor

(iii) 1 - 200 M; t- 5omsec; without divertor

ne(0)(1013 Crn3)

2.08

2.65

4.30

ne(rp)(1013 CC3)

0.10

0.03

0.30

T,(O)(keV)

0.28

0.40

0.80

Te(rP)(keV)

0.02

0.015

0.04

NH(0)(108 cm-3)

N&mJ1o

18.0

cm-3,

TN(O)(eV)

4.91

100.0

14.0

2.50

100.0

1.50

1.50

200.0

Lya emission Ea (1015 phot. cm_2 set-' ster-l)

4.91

2.88

1.02

,(10-6 amps)

4.88

2.83

1.00

1.84

1.43

0.11

P - 10 kW; Is(10-6amps)

S/N

SIP

208.

212.

28.

38.

51.

11.

P - 20 kW: po-6

ampa)

3.46

2.69

0.21

SIN

391.

399.

53.

SIP

71.

95.

21.

calculations of neutral gas transport in PLT due to HUGHES and PosT’~‘].The estimated signal to noise levels on such a discharge in PLT are given in Table 2. together with the plasma and geometric parameters used. The calculated results for the integrated Lya background emission, I?., are in good agreement with the observed value; in all cases the main contribution does indeed arise from the outer 10 cm of the plasma. Even for the low central neutral densities, both S/N and S/F appear favorable; in fact, in model (iii) the signal 1, for P = 10kW is still 2.3% of the background. Figure 7 illustrates S/N and S/F for models (i) and (iii) presented as functions of Lya source power P, and shows the linear behavior for P s 40 kW. (c) Tokamak

fusion test reactor (TFTR)

The estimated central density n,(O) and temperature T,(O) for a high current, quasi-static mode with I = 2.5 MA at t = 400 msec in the projected TFTR experiment are about 5 x 10” cmm3and 10keV respectively.“‘*‘* Assuming that the electron density and temperature profiles will be approximately parabolic as in PLT, and taking again an exponential form for the neutral density profile NH, three possible theoretical models for TFTR have been constructed, the profiles for which are shown in Fig. 8; again in model (iii) the central neutral density is 2 x 10’cm-‘. The estimated signal to noise levels for a Lya fluorescence experiment on this mode of TFTR are given in Table 3, together with the plasma and geometric parameters used. Again, the estimated values of S/N and S/F are very reasonable, even at low Lyu source powers P, where the linear behavior is apparent. Figure 9 shows these estimates for models (i) and (iii) as functions of source power P(kW).

D. W. KOOPMAN CI d.

564

0

‘OOL

F

NH

(I)

0 01

00017 0

IO

20 Fig

30

r

0

I

I

20

40

I

60

r

Fig. 8.

6.

101 o-

S/N(I)

S/N

lO( I-

II3-

l-

OOOll

II)

I( I-

20

40

60 PfkWj Fig. 1.

60

IOC

l-

0

20

40

60

80

P(kW) Fig. 9.

Fig. 6. Possible theoretical profiles for a typical HJ discharge in PLT: I =460 kA. I =300msec. n,(O)= 3x IO”cm ‘. r..tOj = 1.8 keV: parabolic rt,(lO”cm~‘j. parabolic T,tkeVj. exponential NntlO’r’cm~‘): (ij NutOj = lO’cm_‘. (ii) N,(O) = 5 x IO’cm-‘. (iii) Nut01 = 2 x IO’cm ‘. Fig. 7. Estimated PLT: I = 460 kA.

signal

to noise levels for a Lye fluorescence experiment on a typical Hz discharge in Results for models ti) and tiii) of Table 2 presented as functions of Lya source power PtkWj.

I = 3OOmsec.

Fig. 8. Possible theoretical profiles for a projected high current quasi static mode in TFTR: I = 2.5 MA. t = 400 msec, n.(O) = 5 x 1O’x cme3, 7’,(O) = 10 keV; parabolic n,flO’-‘cm-‘); parabolic T,(keV); exponential Nu(lO’Ocm~‘): ti) N”(O) = IO*cm-‘, (ii) N”(O)= 5 X IO’cm-‘. (iii) N”(O)= 2 x IO’cm-‘. Fig. 9. Estimated signal to noise levels for a Lya fluorescence experiment on a projected quasi static mode in TFTR: I = 2.5 MA. I = 400 msec. Results for models (ij and (iii) of Table functions of Lya source power P(kWj.

high current. 3 presented as

100

565

Resonant scattering of lyman alpha radiation Table 2. Estimated signal to noise levels for a Lya fluorescence experiment on a typical Hz discharge in PLT: I = 460 kA, I = 300 msec. Plasma and geometric parameters used : r,,= 4Ocm: MH = 1.0 amu: rh = 0.5 cm: I = .(.Ocm; r.. =2.5cm: rd=60cm; 7,.= Wsec: q = Wsec: r=O.l: 1$=0.01. (ii)

(iii)

3.00

3.00

3.00

0.03

0.03

0.03

Te(0)(keV)

1.80

1.80

1.80

Te(rP)(keV)

0.018

0.018

0.018

N,(0)(108 a~-~)

1.0

0.5

0.2

NH(rP)(lO1' ~rn-~)

1.0

1.0

1.0

Model (I) ne(o)(lo13 cm-3) 13 ne(rp)(10 m-3)

500.

T"(O)(eV)

500.

500.

Lya emission Ea (1014Fhot.cm2sec-1ster-l)

6.23

4.93

4.14

I,(lO_7 amps)

2.72

2.15

1.81

2.10

1.05

0.42

5.7

2.5

7.7

4.9

2.3

4.09

2.04

0.82

P = 10 kW I&&lo-8 amps)

10.

S/N S/F P - 20 kW q10-8

amps)

11.

20.

SIN S/F ___-

5. CONCLUSIONS

15.

AND

4.8

9.5

SUGGESTED

4.5

MEASUREMENTS

A review of Tables l-3 and Figs. 4-9 demonstrates that a Lya resonant scattering experiment with the assumed plasma and geometric parameters should enable central neutral densities as low as 2 x IO’cme3 to be determined on DITE, PLT, or TFTR, provided the source power is above 5 kW. Neutral densities at other radial positions could be obtained at lower Lya power by focusing the source at radial position r and moving the detector to retain the same collection geometry; the background I, then remains constant, whereas the signal Is increases with NH(r). By comparing S/N to S/F, it is apparent that a 1% high frequency fluctuation in the perceived level of I,, would. be more of a problem than the shot noise discuksed by BRETON and P,wwL&) 4 d 10e3would be required before fluctuations could be ignored. Little is known about the high frequency fluctuations in fusion plasmas, although large scale effects have been observed in the 2-50 kHz range’19’ and modest small scale fluctuations, averaged over the volume contribtibg to 4, could possibly provide high frequency components of 4. The absolute magnitudes of the expected signals will required that special attention be given to the electrical properties of the detector and recording components. The scattered current, Is, is likely to range from lo-* to lo-’ amp depending on the Lya source power and the position of the scattering volume in a particular plasma; the background current Zbcould range from IO-’ to 10-5amp under corresponding conditions. The signal, 1s. to be viewed might be as small as 1% of the overall envelope, 4, on which it is superimposed; thus saturation of the detector is to be avoided,. If 500 transmission cables are used, the smallest voltage of interest would be 0.5 pV. too low for direct oscilloscope presentation. Thisobservation suggests that a low noise amplifying photomultiplier. with current gain G, might be used as the detector. To avoid space-charge saturation, the peak anode current of such a tube, I,, = GIb, should be limited to - 10 milliamperes. The estimates of Tables 1-3 indicate that G ranging from 3 x ld to 5 x lo4 would keep I., within the linear range for the chosen experimental parameters, giving back-

D. W. KOOPMAN e/ul.

566 Table 3. Estimated signal quasi-static mode in TFTR: 3.0amu; fb =0.5cm;

to noise levels for a L_va fluorescence experiment on a projected high current. f = 2.5 MA. I = 400msec. Plasma and geometric parameters used: r,, = 85 cm: MH = I = 1Ocm; r, =Scm; rd = 12Ocm; rL = IO-*set; rd= lO_ssec; r=O.l; 4 zO.01.

Model (2) 5.00

T,(O)(keV)

(ii)

(iii)

5.00

5.00

0.05

0.05

10.0

10.0

10.0

T‘,(rP)(ke'J)

0.1

0.1

0.1

N,(O)(lO' cm3,

1.0

0.5

0.2

1.0

1.0

TH(0)(eV)

1000.

1000.

1000.

Lya emission Ea (1014 Phot.cm'sec-'ster-') Ib(10_7 amps)

7.62

5.87

9.20

6.66

5.13

5.12

2.56

1.02

10.5

P = 10 kW Is(lo-S amps) S/N S/F

13. 5.6

7.8

3.6

3.8

2.0

4.94

1.98

P = 20 kW -8 I,(10 amps)

9.88

SIN

26.

S/P

11.

15. 7.4

6.9 3.9

ground signal levels of -0.5 V on 500 systems. Larger currents will be in the range of planar diode operation where Z, as large as I amp can be tolerated and from which a signal level 1, > 10M6 amp can be processed by separate fast amplifiers. Fast response time and modest gain, as would be required for the photomultiplier detector suggested above, can be achieved by modifying conventional photomultiplier currents to use only the first few stages of the multiplying structure@@and high current, low gain photomultipliers with fast response times are now becoming commercially available. Gating of photodetector operation will avoid the drawing of excessive currents during the preliminary portions of the Ib signals.(2’b We conclude with suggestions for measurements on existing fusion plasma facilities which would allow a more detailed assessment of the application of Lya scattering for neutral hydrogen measurements. The first class of measurements would require wavelength resolution of - 0.1-l A, covering a range of - f 50 A around the Lyman alpha line, to examine the emission spectrum of a Tokamak discharge in this range. The relative level of background (bremmstrahlung and recombination radiation) to Lyman alpha intensity should be determined to insure that high-2 impurities do not produce a serious additional contribution to I,. The existence of impurity line spectra, molecular bands, or possible Lya absorption in boundary layers very close to the limiter, would also be determined by these measurements. Time resolution in the millisecond range would be adequate. A transverse scan, followed by Abel inversion analysis, would allow some interpretation of the data in terms of the spatial distribution of contributions to It,. A vacuum spectrograph, followed by a u.v.-phosphor and high-gain photomultiplier, by a u.v.-sensitive OMA, or by a spectrographic plate in conjunction with a fast shutter, would be appropriate for these measurements. The second class of studies would concentrate on the absolute level of It,. The apparatus for this measurement should resemble the detection system of Fig. 2, with a well defined collection geometry. Since the calculations presented in Section 4 indicate that Ir, 2: 10e6- IO-’ amp would

Resonant scattering of lyman alpha radiation

567

be expected from normal Lya emission, with the assumed efficiency and geometry, it appears that a calibrated photo-diode followed by a low-noise amplifier would allow a comparison of the absolute level of I,,. A KBr cathode and a MgFz window on the diode, together with an O2 filter, would limit sensitivity to wavelengths near Lya. From the absolute signal level, the validity of the approximations leading to estimates of Ib could be tested. The final class of measurements would determine the high frequency fluctuation of 4,; because our calculations suggest that the rms value of these fluctuations might be as small as IO-‘amp, a high frequency photomultiplier could supplement data obtainable with the diode used for the absolute signal measurements. From the frequency distribution and amplitude of the fluctuations, and their dependence on Ib, G, the choice of amplifiers, filters, etc., the validity of the shot-noise approximations and the presence of high-frequency plasma oscillations could be assessed. When combined with the wavelength and absolute signal level calculations. more specific designs for the optimum detector system will be possible. Acknowledgements-We would like to thank Drs. K. L. YOUNG.E. HINNOVand S. FIELDINGfor useful discussions and for the provision of experimental and theoretical plasma data prior to publication. Financial support for this work was provided by National Science Foundation Grant ENG 75-02618. A special note of appreciation is due to Ms. MARGARET SMALL,who graciously assisted in the typing of numerous preliminary drafts and to MS ELIZABETH STECHER. who prepared the final manuscript copy. REFERENCES I. 2. 3. 4. 5. 6. 7. 8. 9. IO. II. 12. 13. 14. 15. 16. 17. 18.

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