WDS'09 Proceedings of Contributed Papers, Part II, 115–120, 2009. ISBN 978-80-7378-102-6 © MATFYZPRESS

Ternary Recombination In Deuterium

T. Kotrík, I. Korolov, P. Dohnal, J. Varju, R. Plašil, J. Glosík Charles University Prague, Faculty of Mathematics and Physics, Prague, Czech Republic.

+ Abstract. The recombination of D3 with was studied in plasma over a broad range of pressures and temperatures varying from 77 K up to 300 K using flowing afterglow (FALP) apparatus. Reported is observation of dependence of overall recombination process on temperature, helium buffer pressure and partial + - pressure. The effective plasma recombination rate is driven by binary D3 + e and ternary + - -8 3 -1 D3 + e + He processes with the rate coefficients αBin(300 K) = (2.7 ± 0.9)×10 cm s -25 6 -1 and KHe(300 K) = (1.8 ± 0.6)×10 cm s respectively.

Introduction + + Recombination of H3 and D3 ions with electrons plays an important role in plasma physics, physical chemistry, astrophysics and quantum theory (see reviews [Geballe et al., 2006; Plasil et al., 2002; Larsson et al., 2008]). Despite a great effort over the past years a large discrepancy between the values of the recombination rate coefficients measured in different experiments and between experiments and theory had been remaining. The situation changed in 2001 when Jahn-Teller coupling + + was introduced to the theory of H3 and D3 recombination [Kokoouline et al., 2001]. Today, the + calculated theoretical values of the rate coefficients of the dissociative recombination of H3 ions [Kokoouline et al., 2003; Sanots et al., 2007] are in a qualitative agreement with the storage ring + experiments using rotationally and vibrationally cooled H3 ions. [McCall et al, 2003; Kreckel et al, + 2005]. There are no storage ring data with rotationally cold D3 ions up to now. Plasma experiments with both ions do not give such straightforward agreement with theory [Plasil et al., 2002; Larsson et al., 2008]. + + In our previous studies of H3 and D3 recombination in afterglow plasma (Stationary Afterglow – AISA experiment in Prague) we have observed the dependence of measured recombination rate coefficients on a partial pressure of hydrogen and deuterium, respectively [Plasil et al., 2002; Glosik et al., 2001; Poterya et al., 2002]. The pressure of the helium buffer gas in the experiments varied in the range 200–2000 Pa, the hydrogen and deuterium densities varied from 5×1010 cm-3 up to ≈5×1015 cm-3. In the course of studies we realised that the dependence on hydrogen and deuterium density is caused by a multistep character of the recombination process in He/H2 and He/D2 plasmas. To stress this fact, the symbol αeff was used to denote the measured “effective” recombination rate coefficients. We also measured the dependence of both recombination rate coefficients on temperature. + In the experiments with H3 dominated plasma in He buffer we observed linear dependence of measured αeff on helium density. The results were interpreted by assuming two parallel channels of recombination process in plasma with He buffer gas - binary and ternary. The rate coefficients of both processes were measured [Glosik et al., 2008]. Here we report the results of the experimental study of + the recombination in D3 dominated plasma in He/D2 at temperature 77–300 K.

Experiment The basic experimental apparatus FALP used for recombination rates determination is described in details elsewhere [Smith, 1960; Florescu-Mitchell et al., 2006; Larsson et al., 2008]. For measurements of low recombination rate coefficients (down to 5×10-9 cm3s-1) at relatively high buffer gas pressure (up to 2000 Pa) a new version of apparatus was designed and constructed [Novotny et al., 2006]. For low temperature studies a modification of FALP apparatus – CryoFALP operating in the range of 77–300K was used. Scheme of the new FALP apparatus is shown in Figure 1. Pure helium gas flows through the discharge tube, where a plasma consisting of He+, Hem and electrons is formed by a microwave discharge. Plasma is then driven by the buffer gas pumped by a large Roots pump through a stainless steel flow tube with inner diameter d = 5 cm. Downstream

115 KOTRÍK ET AL.: TERNARY RECOMBINATION IN DEUTERIUM PLASMA

Figure 1. Scheme of Flowing Afterglow with Langmuir Probe apparatus (FALP). The Langmuir probe is movable from the port P2 up to the end of the flow tube. The decay time in the range 0–60 ms is given by the position of the probe. from the discharge region an argon gas is added via the P1 entry port and in series of reactions Ar+ dominated plasma is formed. Further downstream from the Ar port, deuterium is added via the P2 + entry port to already relaxed cold plasma (Te ≈ THe) [Korolov et al., 2008] and D3 dominated plasma is formed. At the end of the flow tube, there is a valve used to adjust the working pressure and the flow velocity to the required values. The experiments are based on the measurements of number density evolution (decay) along the flowing afterglow plasma using the Langmuir probe. The probe is axially movable from the position of the P2 port up to the end of the flow tube (35 cm). The measured velocity of the helium flow is used for conversion of the probe position to the decay time. In figures we arbitrarily use t = 0 at deuterium inlet, upstream from this port t < 0 and downstream t > 0. The kinetics of formation and plasma decay is clear and can be calculated [Florescu-Mitchell et al., 2006; Poterya et al., 2002] The calculated plasma evolution along the flow tube is shown in Figure 2. 12 3 [D ] = 3×1012 cm3 [Ar] = 8×10 cm 2 Detail Ar+ 1010 p = 1600 Pa, T = 250 K 1010 D+ 3

9 + 9 10 10 ] + D + -3 He 3 ArD m + n

He

D [cm 8 2 8 n [cm 10 He+ 10 2 ]

7 7 10 e- 10

-30 -20 -10 0 10 20 30 40 50 012345 time [ms] time [ms] Figure 2. The calculated plasma formation and decay along the flow tube after the addition of Ar and + + D2. In the right panel the detail of transition from Ar dominated to D3 dominated plasma after the addition of deuterium is shown.

Results

Examples of measured electron density decays along the flow tube at several concentrations of D2 are plotted in Figure 3. The apparent recombination rate coefficients (αeff) were calculated from the electron density decays using the advanced analysis [Novotny et al., 2006; Korolov et al., 2008]. In the + data analysis the influence of the formation of D3 dominated plasma on electron density was considered. Plotted is also the decay curve measured in He/Ar afterglow dominated by Ar+ ions in otherwise identical conditions. In Figure 4 the obtained effective recombination rate coefficients are

116 KOTRÍK ET AL.: TERNARY RECOMBINATION IN DEUTERIUM PLASMA

+ plotted as a function of deuterium concentration. In He-Ar-D2 plasma, D3 can collide with D2 prior to recombination with an electron. The number of these collisions (N) depends mainly on + deuterium number density. If D3 ion undergoes several collisions with D2 prior to recombination (that 12 -3 corresponds to [D2] > 2×10 cm in our conditions), i.e. if N > 1, the internal excitation of the ion will be quenched and we can expect the recombining ion to be vibrationally and rotationally thermalized. We will consider in further discussion only the region where the value of αeff is constant, independent 12 -3 13 -3 on [D2] (2×10 cm < [D2] < 10 cm ). The observed difference between the absolute values of measured recombination rate coefficients at different buffer gas pressures and temperatures is evident. The study of αeff = αeff(T,[D2],[He]) in He- Ar-D2 plasma was performed at different temperatures and helium densities. 1010 p ~ 220 Pa, T ~ 77 K D+ 3 Ar+ 109 ] -3

[cm e

n [D ] α 2 eff 12 -3 -7 3 -1 108 [×10 cm ] [×10 cm s ] 0.4 0.3 1.8 0.9 14 1.1 12 -3 38 1.8 [Ar] ~ 1×10 cm 0 1020304050 time [ms]

+ Figure 3. Decays of the electron density in D3 dominated plasma at 77 K and several concentrations of deuterium measured in FALP apparatus. The decay curve measured in Ar+ dominated plasma is also included. The deuterium densities and obtained recombination rate coefficients are indicated. D+ N<1 N>1 N>>1 3 Theory DR at 77 K

10-7 ] s Theory DR at 250 K [cm

eff

α 250 K 77K CryoFALP AISA, 210 Pa 220 Pa AISA, 270 Pa 320 Pa FALP, 1600 Pa 420 Pa 10-8 1011 1012 1013 1014 [D ] [cm-3] 2 Figure 4. Effective recombination rate coefficient (αeff) measured in the flow tube at different He buffer gas pressures and temperatures as a function of deuterium number densitiy [D2][ Novotny et al., 2006; Korolov et al., 2008]. The data from AISA experiment are also shown for comparison. Plotted are also the values of the theoretical recombination rate coefficient calculated for binary dissociative recombination (αDR), at 77 and 250 K [Pagani et al., 2008]. Note that in the theory the considered DR is a binary process and a rate of the binary process is dependent only on a temperature.

117 KOTRÍK ET AL.: TERNARY RECOMBINATION IN DEUTERIUM PLASMA

FALP 8 2.5 + 200 K AISA 250 K + FALP D 250 K Smith 300 K D 77 K 3 300 K 200 K 3 100 K 2.0 6 170 K 170 K ] -1 ] s 250 K 3 -1 s

1.5 3 cm

-7 4 cm 300 K -7 100 K [10 1.0 eff [10 α eff α 2 0.5 77 K RING Theory DR at 300 K 300 K 0.0 0 01234560123456 [He] [1017 cm-3] [He] [1017 cm-3]

+ Figure 5. The dependence of αeff on helium density and temperature. The values of αeff for D3 ions 12 -3 14 -3 were measured at conditions corresponding to the “saturated region” (2×10 cm < [D2] < 10 cm ). Included are data obtained by Smith and Spanel [Smith et al., 1993]. The arrow indicates the value obtained by M. Larsson et al. [Larsson et al., 1997, Le Padellec et al., 1998] in the CRYRING experiment, i.e. the value corresponding to the binary recombination at 300 K. The straight horizontal + line indicates the value calculated for the binary dissociative recombination of D3 ions at 300 K [Pagani et al., 2008]. Dashed lines are linear fits of plotted data; the lines at 170 K and 100 K lead through measured and theoretical values.

The experimental data plotted in Figure 5 show that the measured recombination rate coefficient + αeff depends linearly on helium density [He]. Hence, it is obvious that the recombination of D3 has not only binary, but also a ternary channel with helium acting as a third body. The dependence can be expressed by the formula: α eff = α Bin + He TKT ⋅ ],He[)()( with the coefficients of binary recombination αBin(T) and ternary (helium assisted) recombination KHe(T). The obtained binary and ternary recombination rate coefficients as a function of He buffer gas temperature are plotted in Figure 6 and Figure 7 respectively. The contemporary theoretical values [Pagani et al., 2008] and data obtained in CRYRING experiments [McCall et al., 2003, Kreckel et al., 2005] are also plotted in Figure 6. The agreement is impressive, though noting the fact that the CRYRING experiment probably did not have internally cold ions.

+ Theory DR α D DR 3 ] -1

s 1 3 cm -7 [10 α

FALP CRYRING 0.1 50 100 150 200 250 300 350 T [K] Figure 6. The measured binary recombination rate coefficient, αBin(T). Plotted is also the CRYRING value [Larsson et al., 1997; Le Padellec et al., 1998]. The calculated binary recombination rate coefficient is indicated by the full line [Pagani et al., 2008]. The dashed line denotes the linear fit of measured data.

118 KOTRÍK ET AL.: TERNARY RECOMBINATION IN DEUTERIUM PLASMA

D + 10 3 ] -1 s 6 cm

-25 [10 He

K 1 FALP pressure dependance FALP interpolation CryoFALP continuous measurement

50 100 150 200 250 300 T [K]

+ Figure 7. The ternary recombination rate coefficient, KHe(T), of He assisted recombination of D3 ions. The values obtained from the measured linear dependences of effective recombination rate coefficient on [He] (see dashed lines in Figure 5) are indicated by diamonds, the values of KHe obtained from single measurement at fixed [He] and temperature using the αBin (T) interpolated from the measured values (dashed line in Figure 6) are indicated by triangles. The data measured on Cryo- FALP with continuously increasing temperature are indicated by open circles (for details see text).

The points marked as open circles in Figure 7 where obtained from continuous measurements of temperature evolution in CryoFALP experiment. In these measurements the flow tube was cooled to 77 K and then the flow of nitrogen was stopped. While the temperature of the flow tube was increasing we monitored the temperature and measured αeff(T). Using interpolated values of αBin (T) from our previous measurements (dashed line in Figure 6) we calculated KHe(T) from αeff(T). -8 3 -1 The values obtained for 300 K are: αBin(300 K) = (2.7 ± 0.9)×10 cm s , -25 6 -1 KHe(300 K) = (1.8 ± 0.6)×10 cm s .

Discussion The three-body recombination process with neutral as a third body was previously described by Thomson and by Bates and Khare [Bates et al., 1964]. Typical values of three-body recombination rate coefficients for He as a third body are 10-27 cm6s-1 [Bates et al., 1964]. The ternary process we + observed for D3 recombination is by factor of 100 more efficient; it is evident that observed ternary + process has a different origin. Only very recently we observed a similar fast ternary process for H3 + - recombination in He buffer [Glosik et al., 2008]. By calculating the time delay in H3 + e collisions we showed that the ternary recombination is coupled with formation of long-living highly excited * + Rydberg molecule H3 . In analogy with the model we developed for H3 recombination in plasma we + * assume that in collision of D3 ion with electron neutral D3 can be formed. Life time of this neutral molecule is dependent on electron energy and on internal excitation of ion. At densities typical for our FALP experiment, [He] = 5×1017cm-3, we obtain average time * between collisions of particles with helium τcol = 200 ps. If the life time τ* of D3 molecule is longer or * comparable with 200 ps, the D3 can collide with He prior to its autoionisation, thus influencing the -13 2 recombination process. The cross section of such interaction can be σ3 ≈ 10 cm (see e.g. calculation -8 3 -1 of B. Kaulakys [Kaulakys, 1985]). The corresponding rate coefficient at 300 K is k3 ≈ 10 cm s . As the probability of collision with helium is proportional to [He], the rate coefficient of the overall process will be pressure dependent. In the low pressure limit we will observe a linear dependence on helium density [Atkins, 1986].

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Conclusion + In the study of the recombination process in D3 dominated afterglow plasma we observed linear dependence of the overall recombination (deionisation) rate coefficient on helium density. From measured dependencies we obtained binary and ternary recombination rate coefficients for temperatures from 77 to 300 K. The obtained binary recombination rate coefficient is in agreement with values obtained in CRYRING experiment [Larsson et al., 1997; Le Padellec et al., 1998] and with theoretical values [Pagani et al., 2008]. Further studies of temperature dependency of the rate coefficients of binary and ternary recombination are in progress. -8 3 -1 The obtained binary rate coefficient at 300 K is αBin(300 K) = (2.7 ± 1.3)×10 cm s . The observed ternary recombination is very fast and already at pressures of few hundreds of Pa is dominant over the binary process. The measured ternary recombination rate coefficient is at 300 K KHe(300 K) = (1.8 ± 0.9)×10-25 cm6s-1

Acknowledgments. This work is a part of the research plan MSM 0021620834 financed by the Ministry of Education of the Czech Republic and was partly supported by GACR (202/07/0495, 205/09/1183, 202/09/0642, 202/08/H057), by GAUK 53607, GAUK 124707 and GAUK 86908.

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