A short-pulsed compact supersonic helium beam source for plasma diagnostics

Transcription

1 Plasma Devices and Operations Vol. 14, No. 1, March 2006, A short-pulsed compact supersonic helium beam source for plasma diagnostics D. ANDRUCZYK*, S. NAMBA, B. W. JAMES, K. TAKIYAMA and T. ODA The School of Physics, The University of Sydney, New South Wales 2006, Australia Graduate School of Engineering, Hiroshima University, Hiroshima , Japan Faculty of Engineering, Hiroshima Kokusai Gakuin University, Hiroshima , Japan (Received 4 April 2005; revised 24 October 2005) A short-pulsed (less than 1 ms) compact supersonic helium beam source has been developed for plasma diagnostics purposes. The beam has been characterized experimentally and the results compared with calculations from a simple model that takes into account interaction between the supersonic beam and gas in the region between the nozzle and the skimmer. For a 200 µs driving pulse, a beam of density N> m 3 on the axis, a width of D 1 cm at a distance of 30 cm from the nozzle and a velocity v ms 1 has been achieved. Keywords: Supersonic; Atomic beam; Helium; Magnetic confinement; Plasma diagnostics 1. Introduction There is increasing interest in the use of pulsed atomic beams for edge diagnostics of magnetically confined plasmas. A pulsed helium beam was used by Schweer et al. [1] to measure the electron temperature T e and the electron density n e in the edge plasma of the TEXTOR tokamak [2]. The technique involved interpreting ratios of line intensities in the helium emission spectrum with the aid of a collisional radiative model [3]. Takiyama et al. [4] have proposed using laser-induced fluorescence (LIF) from metastable atoms in a pulsed helium beam to measure radial electric fields in tokamak edge plasmas. The technique, based on detecting the effect of the electric field on the transition probability of the laser-excited forbidden transition 2 1 S n 1 D, where n = 3, 4, 5,...,requires a singlet metastable density n 2 1 S > m 3 [5 7]. Pulsed atomic beam sources consist typically of a nozzle to generate a supersonic beam from a high-pressure gas chamber, followed by a skimmer to produce a collimated diagnostic beam. In the case of a pulsed source the flow through the nozzle is controlled by a pulsed valve. The properties of the resulting beam depend on the source pressure, the nozzle skimmer distance and the volume and pumping capacity of the chamber between the nozzle and the *Corresponding author. daniel@physics.usyd.edu.au Plasma Devices and Operations ISSN print/issn online 2006 Taylor & Francis DOI: /

2 82 D. Andruczyk et al. skimmer [8]. Optimized designs for particular diagnostic requirements have been published [9 13]. The motivation for this work is the construction of a pulsed helium source for radial electric field measurements in the H-1 heliac [14].As the LIF technique uses a laser of pulse length less than 10 ns, the present work is focused on the production of short beam pulses. We show that during a pulse the increasing gas density in the region between the nozzle and the skimmer, referred to as the nozzle chamber, quenches the supersonic beam, leading to a shorter gas pulse than might otherwise be achieved. 2. Theory Isentropic models of the flow from a nozzle into a vacuum indicate that, to achieve a supersonic beam, the ratio P 0 /P b of source pressure to background pressure in the expansion chamber must exceed the value G = ((γ + 1)/2) γ /(γ 1), where γ is the specific heat ratio; G is less than 2.1 for all gases.as the gas leaves the nozzle, its flow velocity increases as the gas expands and cools, achieving a terminal velocity given by [10] v = ( 2R W ) γ 1/2 γ + 1 T 0, (1) where R is the universal gas constant, W is the atomic weight of the gas and T 0 is the source gas temperature. For helium (γ = 5/3) at 300 K the terminal velocity is ms 1 for T 0 = 300 K. The beam density on the centreline is given by [10] N = N 0 ( d x ) 2 C n (γ ), (2) where d is the diameter of the nozzle orifice, x is the distance from the nozzle and C n (γ ) is a constant given by ( (γ 1) A (γ ) 2 ) γ/(γ 1) C n (γ ) =, (3) 2 where A(γ ) is equal to 3.26 for γ = 5/3 [15]. The skimmer selects the central region of the beam. Using simple geometrical considerations, the beam width is given by D = (d + d s)x d s, (4) x s where x s is the nozzle skimmer distance and d s is the diameter of the skimmer orifice. For the present source, the values of d and d s are 0.8 and 1 mm, respectively. When the valve opens, the pressure P in the region between the nozzle and the skimmer will begin to increase because of gas which does not pass through the skimmer. If we make the simplistic assumption that the gas which does not pass through the skimmer instantaneously fills the nozzle chamber, the pressure change in the nozzle chamber is governed by the equation dp dt = kt 0F(t) V S P, (5) V where F(t)is the particle flow rate through the nozzle, V is the volume of the nozzle chamber (figure 1) and S is the pump speed. For a nozzle with orifice area A 0 and constant source

3 Supersonic helium beam source 83 Figure 1. Schematic diagram of the experimental set-up. The nozzle chamber, which is to the left of the skimmer, consisting of a stainless steel T-piece, houses the pulsed valve. Beam measurements were made in the larger test chamber to the right of the skimmer. The pump speed is approximately 66 l s 1 and the volume is approximately 0.23 l. pressure P 0, F(t)is given by F(t) = P 0A 0 (t)a 0 kt 0 ( ) 2 γ/2(γ 1), (6) γ + 1 where a 0 is the speed of sound at the temperature T 0. As the valve has non-zero rise and closing times, the effective value of A 0 will vary with time during the pulse. Integrating equation (5) the pressure in the chamber can be determined as a function of time, which allows the collisional loss of atoms from the supersonic beam to be determined. The mean free path for helium atoms in the beam is given by v 1 λ 12 = πn 2 (r 1 + r 2 ) 2 ( v1 2 + ) 1/2, (7) v2 2 where v 1 is the beam velocity, N 2 and v 2 are the background gas density and thermal speed, respectively, and r 1 and r 2 are the atomic radii of the beam atoms and background gas atoms, respectively. As the beam travels between the nozzle and the skimmer, it will be attenuated by a factor exp( x s /λ 12 ) where λ 12 will be a slowly varying function of time. In reality the pressure in the nozzle chamber will not become uniform instantaneously. The time to reach uniformity will be characterized by the time constant τ, determined by the linear dimensions of the nozzle chamber and the sound speed. This is taken into account in an approximate way in the model by calculating λ 12 using N 2 corresponding to a pressure value P given by P(t) = 1 τ t+τ 0 P i (t τ)dt, (8)

4 84 D. Andruczyk et al. where P i (t) is the solution to equation (5), and P i = 0 for t<τ. A value for the time constant τ (= ms) was determined by calculating the average time that the skimmed gas reflects off the walls of the nozzle chamber and back into the path of the beam. 3. The experiment The beam source uses a pulsed electromagnetic valve with an orifice diameter of 0.8 mm. The opening rise time and the closing time are approximately 160 and 300 µs, respectively. The distance between the pulsed valve nozzle and the skimmer of diameter 1 mm can be varied continuously but is typically set at 30 mm. The interaction volume consists of a small chamber (referred to as the nozzle chamber) which contains the pulsed valve and is 76 mm in diameter and 50 mm in length, with a total volume of 0.23 l. The skimmer is mounted on the common wall between this chamber and a cylindrical test chamber 30 cm in diameter and 60 cm long, as shown in figure 1. A fast ion gauge (FIG) was used to detect the beam in the test chamber. The spatial resolution of the FIG was determined by its 6 25 mm cylindrical collector grid. The gauge was calibrated against a capacitor manometer gauge. The nozzle and test chambers, which communicated via the skimmer orifice, were pumped separately. The approximately 0.23 l volume of the nozzle chamber was pumped by a 200 l s 1 turbomolecular pump. The pump connections, however, reduced this to an effective value of about 66 l s 1 at the entrance to the nozzle chamber (figure 1). The test chamber was pumped by a 1000 l s 1 diffusion pump. A typical FIG signal, shown in figure 2, has two main features: the first peak due to the supersonic component of the beam, and an increasing background due to the diffusion of gas from the nozzle chamber through the skimmer into the test chamber. Figure 2. A typical FIG signal, for which the initial peak is due to the supersonic beam pulse. The driving waveform from the pulsed valve controller (dashed curve) is shown superimposed.

5 Supersonic helium beam source Results and discussion The amplitude of the supersonic pulse becomes independent of the length of the control voltage pulse after about 160 µs, in agreement with the specified opening rise time for the pulsed valve. The amplitude was also found to vary with the nozzle skimmer distance, having a maximum value which depends only weakly on P 0 for x s 30 mm. The full width at half-maximum of the measured beam was 15 ± 2mmatx = 30 cm, in good agreement with the estimate of 13 mm given by equation (4). By recording FIG signals at x = 16 cm and 28 cm for a source pressure of 2 atm and x s = 30 mm, the supersonic beam velocity was found to be about ± 0.05 m s 1, which agrees with the value for terminal velocity given by equation (1). Figure 3 shows a series of pulse shapes for different values of P 0. The peak value is not proportional to P 0 and the pulse width decreases with increasing P 0, suggesting a significant interaction between the supersonic beam and gas build-up in the nozzle chamber. A computer model which takes account of the interaction of the atoms in the supersonic beam with the increasing gas density in the nozzle chamber explains the pulse shape and its dependence on source pressure. In the absence of any interaction with the gas in the nozzle chamber, the centreline density of the supersonic pulse is given by equation (2). However, increasing the gas pressure during the pulse will cause increasing collisional loss of atoms from the supersonic beam, leading to a centreline density given by N 1 = N 0 ( d x ) 2 C(γ ) e x s/λ 12, (9) The model takes into account restricted flow during the opening and closing of the valve by multiplying the unrestricted flow rate by the profile shown in figure 4. The time interval from zero to the end of the flat top corresponds to the duration of the voltage pulse from the Figure 3. Pulse temporal profiles measured using an FIG, for a range of source pressures.

6 86 D. Andruczyk et al. Figure 4. Temporal profile of the area of the valve orifice used in calculations. For a 200 µs controller pulse the valve is fully open for 40 µs after an opening rise time of 160 µs. pulsed valve controller and is referred to as the pulse length. The profile rise is based on a dynamic treatment of the armature (including the poppet) of the valve solenoid, which includes a constant magnetic driving force F B for the duration of the control pulse, a pressure force F P due to the source gas, and a restoring force due to a retaining spring. The displacement of the armature is given by x = F B F P k { 1 sin [ ( k m ) ]} 1/2 t + π, (10) 2 where k and m, the spring constant and mass of the spring respectively, have been measured directly. A value for F B was obtained from the specification that the valve did not open for source pressures above 102 atm. Once the poppet has cleared the valve orifice by a distance equal to the orifice diameter, the flow from the nozzle is assumed to be unrestricted and constant until the end of the control pulse. During the opening stage the profile is assumed to be proportional to displacement, and a linear fall to zero models the closing stage. This model is consistent with the 160 µs valve opening time. An example pulse shape with respect to pulse length is shown in figure 4. This shape is determined by the competition of the increase in the flow from the valve and the attenuation of the beam due to the background gas in the nozzle chamber. Assuming the beam to be travelling at the terminal velocity, individual atoms will take around 17 µs to travel between the nozzle and the skimmer, during which time the pressure in the nozzle chamber will not change significantly. In contrast, the pressure rise will be significant over the duration of the pulse, affecting the pulse shape in the test chamber. Thus the pulse temporal profile is determined from equation (9), with N 0 having the time profile given in figure 4 and N 2 being a function of time from the solution of equation (5). Figure 5 shows calculated pulse profiles for a range of source pressures and for S = 66 l s 1, a volume V = 0.23 l and τ = s. These calculations should be compared with the measurements

7 Supersonic helium beam source 87 Figure 5. Pulse shapes calculated for a range of source pressures. in figure 3. The model explains well the occurrence of the peak density at earlier times in the pulse and reduced pulsed widths as the source pressure increases. Figure 6 compares measurements of the pulse peak amplitude as a function of source pressure P 0 with model calculations. In the absence of an interaction the amplitude would be proportional to P 0 (see the solid line in figure 6). Thus, we conclude that interaction with gas Figure 6. Peak density measurements as a function of source pressure compared with the results of calculations for a variety of input parameters.

8 88 D. Andruczyk et al. Figure 7. Comparison between measured and calculated pulse shapes for a source pressure of 6 atm. Measurements have been scaled in order to agree with the model at the peak value. in the source chamber explains the saturation of the peak amplitude with increasing P 0. The results of calculations depend on values for S and V but are quite insensitive to S for relevant values. The results shown in figure 6 for several values of V show that agreement between measurements and calculations is best for a volume V 0.23 l. Discrepancies between the measurements and model at higher source pressures (P 0 7 atm) are most probably due to the simplistic model for evolution of the effective area of the orifice during the pulse. A comparison of calculated and measured pulse shapes is given in figure 7 for a pulse length of 200 µs, P 0 = 6 atm, S = 66ls 1 and V = 0.23 l. The increasing background following the main peak is likely to be due to diffusion of helium from the nozzle chamber through the skimmer to the test chamber, which is not at present taken into account in the model. 5. Conclusion The time profile of a supersonic pulsed helium beam is affected significantly by the gas build-up during the pulse in the region between the nozzle and the skimmer. A simple model which takes this into account is able to explain the following effects with increasing source pressure: a decrease in the pulse width; the occurrence of the peak at earlier times in the pulse; saturation of the supersonic pulse amplitude. One consequence of this is that the duration of the supersonic pulse is significantly less than would be indicated by the opening time of the valve. This is not necessarily a problem for diagnostics and has the advantage of reducing the amount of gas injected into the plasma. Acknowledgements The authors acknowledge support from the Australian Research Council, the Australian Institute of Nuclear Science and Engineering, the Science Foundation for Physics and the Japan Society for Promotion of Science.

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