Electron-detachment cross sections of halogen negative-ion projectiles for inertial

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2 INSTITUTE OF PHYSICS PUBLISHING Plasma Phys. Control. Fusion 46 (2004) PLASMA PHYSICS AND CONTROLLED FUSION PII: S (04) Electron-detachment cross sections of halogen negative-ion projectiles for inertial confinement fusion M M Sant Anna 1, F Zappa, ACFSantos 2,ALFdeBarros, W Wolff, L F S Coelho andnvdecastro Faria Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ , Brazil mms@if.ufrj.br Received 26 March 2004 Published 18 May 2004 Online at stacks.iop.org/ppcf/46/1009 DOI: / /46/7/001 Abstract Negative-ion beams have recently been suggested as sources of high-energy heavy atoms to be used as drivers for inertial confinement fusion (ICF). Owing to their electron affinities limited to a few ev, anions can be efficiently photo-detached in the vicinity of the fusion chamber, with the resulting highvelocity neutral projectiles following ballistic trajectories towards the hydrogen pellet target. Electron-detachment cross sections are needed as parameters to estimate the beam attenuation in the path from the ion source to the hydrogen pellet. Halogen anions are possible projectile choices. In this paper we present experimental data for total electron-detachment cross sections for F, Cl,Br and I ions incident on N 2, in the kev u 1 energy range. Our measurements can benchmark theory on anion electron detachment at intermediate to high velocities. Comparison between different projectiles shows very similar collision velocity dependencies. A simple geometrical scaling is presented, providing an estimate for electron-detachment cross sections at the MeV u 1 energy range. The presented scaling indicates that the vacuum requirements due to the use of halogen anions for ICF are less critical than previously suggested. (Some figures in this article are in colour only in the electronic version) 1. Introduction The inertial confinement fusion (ICF) approach to sustainable nuclear fusion is based on the use of high-velocity high-current ion beams focused, during a small time interval, on a hydrogen 1 Author to whom any correspondence should be addressed. 2 Present address: Centro Federal de Educação Tecnológica de Química, Rio de Janeiro, Brazil /04/ $ IOP Publishing Ltd Printed in the UK 1009

3 1010 M M Sant Anna et al pellet that is the fuel for the nuclear fusion. Major difficulties, however, arise from Coulomb repulsion between projectile charged particles (the space-charge effect), beam self-magnetic fields and beam plasma instabilities, which are relevant for high-current ion beams and degrade the beam transport and focusing characteristics (Grisham 2003). One strategy to overcome these difficulties is to use a focusing lens just outside the fusion chamber and, subsequently, neutralize the beam, in the so-called neutralized-ballistic transport (NBT) (Welch et al 2002). Traditionally, NBT employs positive projectiles that capture electrons. The possibility of using negative-ion beams has recently been raised due to their binding energies of not more than a few ev (Grisham 2001), as these low binding energies allow for an efficient neutralization of the anions by photo-detachment. Halogen negative ions were pointed out as good candidates for the production of the high-current beams needed for ICF (Grisham 2003, Hahto et al 2003). In order to explore the practical upper limits for the ion current of negative halogen beams intended for ICF, recent measurements were made in the Plasma and Ion Source Technology Group of the Lawrence Berkeley National Laboratory (Hahto et al 2003). Although only chlorine ions were studied due to instrumental limitations in the Hahto et al (2003) experiment, the heavy atoms bromine and iodine are more appropriate for ICF than fluorine or chlorine. There are critical issues when considering the use of negative-ion beams in ICF devices (Grisham 2001, Grisham 2003). Vacuum requirements for negative-ion beam transport, in particular, are more stringent than for the positive-ion counterparts, due to higher chargechanging cross sections. The cross sections for negative-ion detachment (or stripping), for intermediate and high velocities, are larger than the cross sections for electron capture of an equivelocity singly charged positive projectile. This may cause the loss of an important fraction of the beam in collisions in the first few centimetres after the ion source extractor and in the transport of the beam throughout the accelerator system. The hydrogen pellets are located inside a target chamber. The chamber wall has to be protected from radiation, neutrons and debris arising from the fusion reaction. In scenarios currently proposed, this protection is provided by liquid jets of molten FLiBe salt, resulting in a vapour environment dominated by BeF 2 gas (Celata et al 2003). It is then crucial that only a small fraction of the beam is neutralized before the last focusing lens, in a region where certainly there will be gases originating from the molten FLiBe (Grisham 2001). It is convenient to analyse the effect of projectile electron detachment in three different stages of an ICF device. In the first stage, close to the exit of the ion source, the projectile energy is still of the order of a few tens of kev u 1 (Grisham 2003). In a second region, where the beam is accelerated and guided towards the fusion chamber, the electron detachment cross sections are quite different. This second region should have a path length of the order of 1 km (Grisham 2003). The final stage, the region close to the fusion chamber, has to be considered with special care due to high BeF 2 pressures (Celata et al 2003, Grisham 2003). In this paper, we present experimental data for total electron-detachment cross sections for F,Cl,Br and I ions incident on N 2. Molecular nitrogen was chosen as target for two reasons. First, it is a typical residual gas in the long vacuum beamlines. Second, N 2 is relatively similar in size and in number of electrons to BeF 2 molecules (Grisham 2001), but the experimental manipulation of N 2 is much more convenient. It is worthwhile pointing out that current evaluations of negative-ion beam drivers for ICF (Grisham 2003) use as parameters semiempirical estimates based on 3.4 MeV u 1 electron-loss cross sections for the projectiles Kr 7+ and Xe 11+ incident on N 2 (Mueller et al 2001). These cross sections for multiply charged projectiles were used only because there are currently no accelerators capable of providing singly charged heavy ions at the energies (20 40 MeV u 1 ) appropriate for ICF (Grisham 2001, Mueller et al 2001, 2002, DuBois et al 2003). Calculations

4 Halogen electron-detachment cross sections for ICF 1011 Figure 1. Schematic diagram of the experimental setup. for projectile electron loss valid for both intermediate-to-high and high collision velocities are feasible (Montenegro et al 1992, 2002, McGuire 1997), though few have been made specifically for anionic projectiles (Kaganovich et al (2003) and previous results reviewed in Risley (1980), Champion (1982), Esaulov (1986), McDaniel (1994)). Comparison between experimental data and theory for singly charged projectiles, thus, cannot be done presently in the MeV u 1 energy range. It is the intermediate-to-high velocity regime (E tens of kev u 1 ) that offers the possibility of this direct experiment theory comparison of cross sections. The energy range of our measured cross sections extends from 0.94 to 74 kev u 1. Thus, our data can be used to estimate the beam fraction that is lost in the vicinity of the negative-ion source and benchmark calculations for the tens of kev u 1 energy range. Furthermore, comparison among the different studied projectiles shows very similar collision velocity dependencies. A simple geometrical scaling is presented and compared with data for H electron detachment to provide an estimate for total electron-detachment cross sections of halogen anions colliding with small molecules at the MeV u 1 energy range. This estimate allows the analysis of vacuum requirements for ICF due specifically to the use of halogen anion projectiles. 2. Experimental method The experimental setup was described in detail elsewhere (Luna et al 2001a, b, Zappa et al 2003) and only the main features are outlined here. The experiment was conducted at the Universidade Federal do Rio de Janeiro (UFRJ), using a 1.7 MV Tandem accelerator from the National Electrostatics Company. The accelerator is equipped with a negative-ion source based on the sputtering of material from a sample containing the element of interest. It has a cylindrical gas stripper 1 cm wide and 47 cm long placed at the high-voltage terminal, between the two accelerator tubes (around 2 m each) (figure 1), and pumped by two 500 litre s 1 turbomolecular pumps located at each extremity of the tandem. The stripper gas, N 2, can be fed in from the exterior of the accelerator through an electronically controlled needle valve. To determine the electron-detachment cross sections we used a beam attenuation technique. We explore the fact that the beam energy is low at the exit of the ion source and at the momentum-analysing magnet, and high at the collision chamber (the tandem gas stripper). The low-energy negative-ion beam from the ion source is first accelerated and then collides with the N 2 gas target. After the collision, the negative-ion beam is decelerated and selected by a magnet. Finally, the attenuated current is measured (figure 1).

5 1012 M M Sant Anna et al 2.0 Cl - + N 2 Cl - current (arb. units) 1.0 I=I 0 e - σ d Π E P =400 kev x x10 15 Π (cm -2 ) Figure 2. Typical beam attenuation curve for a 400 kev Cl beam. The solid line is the exponential fit to the data, from which the value of the detachment cross section is obtained. The anion beam is attenuated as the pressure in the gas cell is varied. (A typical beam attenuation curve is shown in figure 2.) The measured anion current, I, is plotted against the parameter, defined as the product of the gas density in the collision cell and its effective length. The detachment cross section (σ d ) is obtained by adjusting an exponential decay function to the attenuated current: I = I 0 e σ d (1) The actual value of the initial current, I 0, may depend on the beam focusing conditions, but is irrelevant to the determination of σ d. Around 200 pressure points are used for each attenuation curve, resulting in cross section standard deviations of the order of 1%. A method was developed to obtain from the pressure at the tandem exit, using an auxiliary experiment with an H beam and the well known charge-changing cross sections for hydrogen (Luna et al 2001a, b, Zappa et al 2003). The systematic errors, mainly due to this pressure calibration procedure (Luna et al 2001a, b, Zappa et al 2003), are at most 10% and affect all projectiles by the same amount. 3. Results and discussion Our measured total electron-detachment cross sections for F,Cl,Br and I ions incident on N 2 are presented in table 1. The cross sections are plotted in figure 3 as a function of the projectile velocity in atomic units (v 0 = ms 1 ). Results available in the literature for lower velocities (Lichtenberg et al 1980) are also plotted, showing good agreement in the overlapping velocity region. From figure 3 it can be seen that our measurements present a smaller dispersion than the lower velocity data of Lichtenberg et al (1980), especially for Cl.

6 Halogen electron-detachment cross sections for ICF 1013 Table 1. Measured total electron-detachment cross sections, σ d ( cm 2 ), for F,Cl,Br and I projectiles incident on N 2. σ d ( cm 2 ) Energy (kev) F Cl Br I Electron detachment in the tens of kev u 1 energy region Also shown in figure 3 are the detachment cross sections for H projectiles incident on N 2 from the data compilation of Nakai et al (1987). Grisham (2003) suggested that because the electron affinity of the halogen anions is around four times larger than for H (Andersen et al (1999), see table 2), the electron-detachment cross sections should be smaller for halogen anions than for H, for the same projectile velocities. Therefore, based on a scaling of the cross sections with the inverse of the projectile binding energy, valid for positive-ion projectiles, his work assumed that electron stripping at the kev u 1 energies should be less important for halogen anion sources than for the commonly used high-current H and D ion sources. Our data show that this is not the case for halogen negative-ion projectiles. For projectile velocities larger than 0.3v 0 ( ms 1 ), the detachment cross sections for the I are actually larger and not smaller than those for equivelocity H projectiles (figure 3). However, cross sections are still of the same order of magnitude, and the use of halogen negative ion sources for ICF seems to be feasible concerning vacuum conditions close to the ion source.

7 1014 M M Sant Anna et al 3x10-15 X - + N 2 σ d (cm 2 ) 1x v (atomic units) Figure 3. Experimental total electron-detachment cross sections for negative ion projectiles incident on N 2. This work (filled symbols): squares, I ; circles, Br ; up triangles, Cl ; inverted triangles, F ; Lichtenberg et al (1980) (open symbols): squares, I ; circles, Br ; up triangles, Cl ; Nakai et al (1987) (a compilation of experimental data for the H projectile): full line. A typical error bar, including normalization procedure, is shown only for the present F data. Table 2. Electron affinities and ionic radii for H,F,Cl,Br and I anions. Ionic radius (Å) Electron affinity Shannon (1976), Anion Andersen et al (1999) Miessler and Tarr (1998) H F Cl Br I Electron detachment in the tens of MeV u 1 energy region In order to estimate the fraction of the beam lost during its acceleration and transport towards the fusion chamber, it is necessary to know the detachment cross sections for atomic and molecular targets corresponding to the beamline residual gases. Close to the fusion chamber, BeF 2 will be a major constituent of the beamline gas mixture, being originated in the FLiBe molten salt used in the fusion chamber. Electron-detachment cross sections for an N 2 target should provide a good approximation for BeF 2 cross sections (Grisham 2001). Although our data are limited to the tens of kev u 1 energy region, three points stimulate the use of these data to estimate the cross sections in the tens of MeV u 1 energy region. The first point is the similarity of the velocity dependencies for the different projectiles (figure 3). The four curves have basically the same shape, differing only in absolute values. Second, the detachment cross sections, for velocities larger than 0.4v 0, are very close for H and for Cl

8 Halogen electron-detachment cross sections for ICF 1015 H σ (cm 2 ) H v (atomic units) Figure 4. Same as figure 3, and lozenges, total electron scattering cross sections (Blaauw et al 1980); shaded circles, Br +N 2, semiempirical (Grisham 2003); shaded squares, Born approximation for I + N, single-detachment cross section for an atomic nitrogen target multiplied by 2 (Kaganovich et al 2003); dashed line, a compilation of experimental data for H 0 projectile electron loss (Nakai et al 1987). The error in the H data compilation (, Nakai et al (1987)) is 5% for v<7and 20% for v of the order 20. and Br projectiles. The cross sections for I are about 20% larger and for F 50% lower, when compared with the H projectile (figure 3). There are many published experimental studies for H electron detachment on N 2 at both intermediate and high velocities. These include an experimental data compilation by Nakai et al (1987) that presents a single analytical expression for intermediate and high velocities. Finally, data for total (elastic + inelastic) electron projectiles scattering by N 2 (Blaauw et al 1980) are very close to equivelocity H projectiles (figure 4). This shows that the impulse approximation (Dimitriev and Nikolaev 1963, Melo et al 1999) is already valid in the intermediate-to-high velocity range, and that the dynamics of the collision should be similar for all the equivelocity anionic projectiles. Figure 4 shows electron-detachment cross section calculations for I + N (Kaganovich et al 2003) (multiplied by 2 in order to estimate the cross sections in N 2 ) and semiempirical estimates for Br +N 2 (Grisham 2003). The I +N values are obtained from Born approximation and are slightly above the H data, just like the lower energy data. The Br +N 2 results, on the other hand, are about a factor of 60 higher than the H results and are probably overestimated (see table 3). This discrepancy is particularly critical, since a current evaluation of the role of negative-ion beams as drivers for heavy ion fusion (Grisham 2003) uses these Br +N 2 cross sections, as discussed in section Geometrical modelling of cross sections to evaluate vacuum constraints A geometrical scaling is proposed here for the detachment cross sections for different projectiles. It is based on the cross section curves close to the velocity for which they reach

9 1016 M M Sant Anna et al Table 3. Comparison of high-velocity electron-detachment cross sections for Br and I projectiles obtained by different methods. σ d (10 16 cm 2 ) Energy Semiempirical model Born Equation (2) scaling MeV u 1 Anion Grisham (2003) Kaganovich et al (2003) Present work I 4.94 a Br I 0.16 a Br a Single-detachment cross section for atomic hydrogen, multiplied by 2. 1 σ / π ( r P + r T ) X - + N r T r P v (atomic units) Figure 5. Same as figure 4 but scaled by geometrical factor (see text for details). The electron projectile data ( ) where plotted is divided by the same factor as the H projectile, to emphasize the similarity of these two projectiles. their maxima (around 0.4v 0 ). At that velocity, the probability of the projectile losing its weakly bound electron is high if the collision impact parameter is small enough that there is overlap between the projectile and target electron clouds (see inset of figure 5). Figure 5 shows cross sections scaled by the factor π (r P + r T ) 2, where r P and r T are the average radii for the electronic clouds of projectile and target, respectively. For r P of the halogen anions, we have used values from the literature (Shannon 1976, Miessler and Tarr 1998). For the H ionic radius, as Shannon points out, there is some controversy. We have used the value 1.53 Å (Morris and Reed 1965). Using an alternative radius, r H = 1.40 Å (Gibb 1962), would cause only small changes for the H projectile scaling. Determining the target effective radius, r N2, is less straightforward. We have modelled the N 2 molecule as two spheres with radii equal to the average Hartree Fock value for N atoms (r N = 0.75 Å) (Fischer 1977). The distance between the partially overlapping N spheres is the N N equilibrium length in N 2 : D N N = Å

10 Halogen electron-detachment cross sections for ICF 1017 (Miessler and Tarr 1998). The shadow produced by the two spheres depends on the spatial orientation of the molecule. We have averaged the result over all orientations of the molecular axis and obtained an area equivalent to the area of the shadow of a single sphere with r N2 = 0.97 Å. This value, which was used in the scaling, is smaller than the ionic radii of the presently studied projectiles (table 2). The electron-detachment cross sections for high velocities can, thus, be approximated by the scaling rule σ X = (r X + r N 2 ) 2 (r H + r N2 ) σ 2 H (2) with the value for r X given in table 2 and r N2 = m. A convenient analytical expression for H total electron-detachment in N 2 (single detachment + double detachment), from Nakai et al (1987), is reproduced below for completeness: where σ H σ 10 = σ 10 H + σ 11 H (3) H ( cm 2 (E 1 /25) ) = 438 (4) 1+(E 1 /0.840) (E 1 /41) 2.1 H ( cm 2 (E 2 /25) 0.48 ) = 1.77 (5) 1+(E 2 /152) 2.00 σ 11 with E 1 = E and E 2 = E High-velocity electron-detachment cross sections for the negative ions are essential parameters to estimate the beam-attenuation fraction in the long accelerating path towards the fusion chamber. Our scaling provides estimates for these cross sections. Grisham (2003) uses the 40 MeV u 1 Br +N 2 detachment cross sections, obtained by a semiempirical analysis based on Kr 7+ +N 2 and Xe 11+ +N 2 data (Mueller et al 2001), to evaluate the feasibility of using negative-ion beams as drivers for ICF. He determines the beamline pressure necessary so that the incident beam is attenuated by only 5%. With his semiempirical estimate for the detachment cross sections (table 3), he gives a pressure limit of P beamline = Torr, for a 1 km beamline. Our scaling results in a cross section lower by a factor of 16 and, therefore, a critical pressure of P beamline = Torr. The former pressure estimate is moderately challenging, as pointed out by Grisham (2003), while the latter, from our scaling, points to a situation easily achieved with present vacuum technology. Multiple electron detachment is in principle more relevant for the halogen anions than for H projectiles. The many-shell halogen anions have more electrons in the outer shell, and innershell electrons with translational kinetic energies greater than their binding energies (Mueller et al 2001, Grisham et al 2003). This effect suggests that experimental cross sections should be higher than the estimates from our scaling. However, data for 3.4 MeV u 1 Kr 7+ +N 2 (Mueller et al 2001) show a ratio of multiple-to-single detachment cross sections of 0.79, which should increase our estimate by less than a factor of 2, still leading to relatively low critical pressures. Moreover, the calculations of Kaganovich et al (2003) for 25.2 MeV u 1 I + N (multiplied by 2, to simulate a nitrogen molecule) include the contribution of inner shells and are consistent with our scaling from equation (2) (see table 3). It is also possible to use our scaling to estimate the critical pressure inside the fusion chamber, although an additional approximation is necessary. After being photo-detached, close to the fusion chamber, the resulting neutral beams of high-velocity halogen atoms must follow ballistic trajectories towards the hydrogen pellets. The projectiles are now neutral and cross sections for neutral projectile electron loss are needed. However, these should be smaller

11 1018 M M Sant Anna et al than cross sections for the corresponding anion (see figure 4 for H and H 0 projectiles). Thus, we use the negative projectile cross sections as an approximation for the neutral projectile cross sections. Grisham also determines the fusion-chamber pressures necessary so that the incident neutral beam is attenuated by only 5%. He uses as an estimate for the projectile electron-loss cross sections of cm 2 from his semiempirical analysis for 40 MeV u 1 Br +N 2 detachment cross sections (table 3). For a 3 m radius target chamber he presents a 5% attenuation pressure of P chamber = Torr. This pressure requirement is critical, due to the expected experimental chamber pressures of the order of Torr (almost two orders of magnitude higher). However, discrepancies between the Br +N 2 and all other data and calculations shown in figure 4 and table 3 suggest that the pressure calculated by Grisham is overestimated. Using the scaling of equation (2), we determine the pressure P chamber = Torr for 5% beam attenuation. This result indicates that halogen anions are more suitable for ICF drivers than previously suggested by Grisham. 4. Conclusion In this paper, we presented experimental data for total electron-detachment cross sections for kev u 1 F,Cl,Br and I ions incident on N 2. Molecular nitrogen was chosen as target not only because it is a common residual gas in the vacuum beamlines, but mainly due to its similar size and easier manipulation, when compared to the BeF 2 molecules present in the FLiBe vapour environment of ICF chambers (Grisham 2001). Current evaluations of the potential role of negative halogen ions as driver beams for ICF (Grisham 2003) use as parameters electron-loss cross sections for multiply charged projectiles (Mueller et al 2001) and lack experimental data for electron detachment from the singly charged anions. The present data are useful to estimate the beam fraction that is lost in the vicinity of the negative-ion source and provide a benchmark for calculations of halogen electron-detachment cross sections in the intermediate-to-high velocity regime. Besides the experimental data presented here, we have also made a simple geometrical model for their description, useful for ICF studies. The scaling presented indicates that the vacuum requirements due to the use of halogen anions for ICF are less critical than previously suggested and, therefore, that halogen anions are even better candidates for ICF drivers than originally suggested by Grisham (2001). Acknowledgments This work was partially supported by the Brazilian agencies CNPq, FUJB and FAPERJ. References Andersen T, Haugen H K and Hotop H 1999 J. Phys. Chem. Ref. Data Blaauw H J, Wagenaar R W, Barends D H and de Heer F J 1980 J. Phys. B: At. Mol. Phys Celata C M et al 2003 Phys. Plasmas Champion R L 1982 Adv. Electron. Electron Phys Dimitriev I S and Nikolaev V S 1963 Sov. Phys. JETP DuBois R D et al 2003 Phys. Rev. A Esaulov V A 1986 Ann. Phys. Fr Fischer C F 1977 The Hartree Fock Method for Atoms (New York: Wiley) GibbTRP1962 Prog. Inorg. Chem Grisham L R 2001 Nucl. Instrum. Methods A

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