Recombination experiments at CRYRING - Springer Link

Hyperfine Interactions 114 (1998) 237–243

237

Recombination experiments at CRYRING W. Spies a , P. Glans a , W. Zong a , H. Gao a,∗ , G. Andler b , E. Justiniano c , M. Saito d and R. Schuch a,∗∗ a

Department of Physics, Institute of Atomic Physics, Stockholm University, S-104 05 Stockholm, Sweden b Manne Siegbahn Laboratory, Stockholm University, S-104 05 Stockholm, Sweden c Department of Physics, East Carolina University, Greenville, NC 27858, USA d Laboratory of Applied Physics, Kyoto Prefectural University, Shimogamo, Sakyo-ku, Kyoto 606, Japan

Recent advances in studies of electron–ion recombination processes at low relative energies with the electron cooler of the heavy-ion storage ring CRYRING are shown. Through the use of an adiabatically expanded electron beam, collisions down to 10−4 eV relative energies were measured with highly charged ions stored in the ring at around 15 MeV/amu energies. Examples of recombination measurements for bare ions of D+ , He2+ , N7+ , Ne10+ and Si14+ are presented. Further on, results of an experiment measuring laser-induced recombination (LIR) into n = 3 states of deuterium with polarized laser light are shown.

1.

Introduction

There are three fundamental processes in which a free electron can recombine with an ion, namely radiative recombination (RR), dielectronic recombination (DR), and three-body recombination (TBR). In RR the free electron is captured to a bound state of the recombined ion and a photon is emitted balancing the energy and momentum of the process. DR is a two-step process where photon emission occurs from an intermediate doubly excited state. Finally, TBR involves two free electrons, one being captured by the ion and the other carrying away the excess energy and momentum. Recombination rates are of great importance for plasma diagnostics [1]. For example, astrophysical plasmas are investigated through analysis of their radiation spectra and to correctly model these plasmas, accurate knowledge of electron–ion recombination is required [2]. Recent studies have yielded measured recombination rates at very low relative velocities that are much larger than what theory predicts [3,4]. This puzzling phenomenon has drawn much attention both theoretically [5–8] and experimentally [9–11]. A proper understanding of this effect is very important since incorrect rates may lead to wrong determinations of the composition of astrophysical objects. Indeed, a discrepancy (by a factor of 5) of abundances determined from recombination as opposed ∗ ∗∗

Present address: Department of Physics and Astronomy, University College London, WC1E 6BT, UK. Corresponding author. E-mail: [email protected].

 J.C. Baltzer AG, Science Publishers

238

W. Spies et al. / Recombination experiments at CRYRING

to collisionally excited lines was recently reported in [12]. For ions with a complex electronic structure, such as Ar13+ [9], U28+ [3], and Pb53+ [13], most of the enhanced rates may be attributed to DR resonances occurring at very low relative energies. However, for bare ions DR is not possible and the enhanced rates found for these ions still pose an open and challenging problem. In order to investigate further the mechanism behind the enhancement we made a systematic study of bare ions [14]. The ions D+ , He2+ , N7+ , Ne10+ , and Si14+ were chosen because: (1) there is no uncertainty about their “effective charge” [15], and no DR resonances contribute to the measured rates; (2) the nearly constant charge to mass ratio Z/A ≈ 0.5 allows the different ions to be stored and cooled sequentially without substantial changes of the ring parameters; (3) D+ is well investigated and thus can serve as a benchmark system. Another effect that may be related to the enhancement found in RR studies is the below-threshold gain found in laser-induced radiative recombination (LIR). If (radiative) recombination reactions take place in an intense laser field, capture into specific final states of the ion may be enhanced by stimulated photon emission leading to a gain for the rate of stimulated population of a given state over the spontaneous reaction rate. LIR is a resonant process, as the laser wavelength must match the corresponding wavelength of the free-bound RR transition. One outcome of LIR experiments has been the observation of below-threshold gain [16–18]. This effect has been attributed to the space-charge field of the electron beam and to inhomogeneities of the guiding magnetic fields. However, recent studies have shown that this explanation is not entirely satisfactory [17,18]. TBR and collective screening effects may also lead to additional intensities in the reaction rate. However, before these contributions can be studied other effects have to be understood, e.g., the influence of the polarization direction of the laser light. Therefore we have used linearly polarized laser radiation and intentionally enhanced the space-charge field to investigate possible directional effects in the below-threshold gain. 2.

Experimental setup

The experiments were performed with the CRYRING storage ring at the Manne Siegbahn Laboratory at Stockholm University. The ions, produced from an EBIS or a Penning ion source, were injected into the ring, after pre-acceleration to 300 keV/amu in an RFQ, and accelerated to 15 MeV/amu (RR) or 23 MeV/amu (LIR) prior to storage. During electron cooling, the ions were merged over an effective length of ` = 0.8 m with a velocity matched electron beam, confined by a solenoidal magnetic field of 0.03 T to a diameter of 40 mm. The electron densities were about 2×107 particles/cm3 and electron beam temperatures, obtained from fits of DR resonances in C3+ and Ar13+ , were T⊥ = 10–20 meV/kB (transverse) and Tk = 0.1–0.15 meV/kB (longitudinal).


239

The rates of recombined ions were measured at the exit of the first bending magnet after the electron cooler by a surface barrier detector with unity detection efficiency. In the LIR experiment additionally a laser beam coming from an optical parametric oscillator (OPO) was aligned to overlap with the ion beam in the cooler [19]. The alignment was made with the help of two horizontal and two vertical scrapers. By tuning the laser from 654.5–660.5 nm, which translates to 817–824.5 nm in the rest frame of the ions due to Doppler shift, the wavelength was scanned around the threshold of 820.36 nm for capture into the n = 3 state of D+ . The laser beam from the OPO had a pulse width of about 4 ns, a power of about 95 mJ and was to a high degree (>80%) linearly polarized. By the use of a Glan polarizer the beam was polarized completely and the direction of the electric vector (~ε ) was chosen with a polarization rotator. To increase the space-charge field seen by the ions we then shifted the electron beam out of the center of the beam tube by 2.5 mm to investigate possible directional effects. 3.

Enhancement of spontaneous recombination rates

As an example for the enhanced RR rates measurements performed at CRYRING are shown in figure 1 [14]. The recombination rate coefficients of D+ , He2+ , N7+ and Si14+ are shown as function of the relative energy, together with corresponding theoretical RR predictions. The measured rate coefficients are absolute except for Si14+ which is normalized to the high energy part (>10 meV) where no enhancement exists for the other ions and also has not been observed in previous measurements [9,20]. The experimental uncertainty is about 10%, and reflects mainly the uncertainty in the effective interaction length. In the calculation of RR, the semiclassical Kramers cross section corrected by the Gaunt factor [21] is used, and convoluted with the electron velocity distribution characterized by the beam temperatures T⊥ and Tk . In the regime of energies below 10−3 eV, the average center-of-mass energies of the electron–ion systems should be constant and close to kT⊥ . It is therefore striking that the recombination rates change strongly for variations of E well below kT⊥ . An explanation for the latter could be given by considering the guiding solenoidal field of 300 G in the cooler which forces the electrons onto cyclotron orbits with a mean radius of about 8 µm, less than the average distance between electrons of 23 µm. The transverse motion could thus be confined in these orbits and the electrons collide with each other mainly via the longitudinal direction, resulting in the observed characteristics of the enhanced rates at such small energies. Three-body recombination is another proposed mechanism for the enhanced rates of bare ions. In this process electrons are captured preferably into high n states whereas in an RR process electrons are captured mainly in low n states. In the dipole magnet following the electron cooler high Rydberg states above a level nmax become field ionized unless they de-excite (radiatively) to levels below nmax before reaching the magnet. Different models have been compared in [14], however, they are very sensitive to the selection of the value of nbot below which all states are assumed to

240


Figure 1. Measured recombination rate coefficients of D+ , He2+ , N7+ and Si14+ [14]. The curves are calculated RR rates based on electron temperatures of T⊥ = 10 meV/k and Tk = 0.1 meV/k for He2+ and Tk = 0.12 meV/k for other ions. The “relative” energy is calculated from the mean longitudinal velocity (vk ) component difference between electrons and ions.

de-excite to levels below nmax . It has also been proposed that de-excitation could be enhanced by external fields [5]. Recent calculations [7] show that TBR may not contribute significantly enough to explain the observed enhancement effect.

4.

Polarization dependence of laser-induced recombination

The gain in LIR is defined as the ratio between the induced rate (Rnind ), with the laser on, and the RR rate (Rspo ), with the laser off. We used the following expression for the theoretical gain curves:


X Rnind Gn (ε) = spo = G0n` R `=0 Z ∞ × n−1

Z

Z

π

241

2π

σn` (ρ) sin φ φ=0

Eγ =E0 −εsp sin(ν/2)

θ=0

f (εt , φ, θ)g(Eγ ) dEγ dφ dθ,

(1)

where ε is the energy with respect to the ionization energy (E0 ), Eγ corresponds to the photon energy, σn` (ρ) is an anisotropy parameter obtained from the differential photoionization cross-section, f (εt , φ, θ) describes the flattened velocity distribution of the electrons (kT⊥ = 20 meV and kTk = 0.15 meV were used), and g(Eγ ) is a normalized Gaussian which accounts for the linewidth of the laser. The angles ρ and ν can be expressed in terms of θ and φ, and εt = Eγ − E0 + εsp sin (ν/2), where εsp accounts for the fact that an external electric field lowers the ionization threshold [16]. The factors G0n` contain the Rspo part and some other constants. These factors also include the laser intensity. However, since the laser intensity is well-above the saturation level, the saturation intensities for the 3s, 3p and 3d levels are used (intensities of 0.85, 2.53 and 1.97 MW/cm2 were used). In figure 2 theoretical gain curves for an assumed electric field of 15 V/cm at three different angles χ, denoting the angle between the polarization vector and the

Figure 2. Theoretical gain curves for three different polarization angles (χ) before convolution with the laser bandwidth of the OPO (the lines with a sharp onset at −3 meV) and after convolution (lines with a smooth onset).

242


Figure 3. Energy dependence of the measured gain for four different polarization angles (χ) compared to calculated gain curves for polarization angles of 0◦ and 90◦ .

direction of the electric space-charge field, are shown. The three curves having a sharp onset at about −3 meV were obtained assuming a narrow laser bandwidth whereas the other curves show the gain after convolution with the actual bandwidth of the OPO laser. In the case of narrow laser bandwidth, our theory predicts a significant dependence on the angle χ with a notable double-peak structure for χ = 0◦ . To explain this one has to consider that the photoionization cross-section σn` (ρ) has its maxima at ρ = 0◦ and 180◦ . The relation between ρ an ν then leads to maximum values for the flattened velocity distribution (for χ = 0) roughly at Eγ = E0 − εsp and Eγ = E0 . However, after convoluting with the actual bandwidth, which is about 2 nm for wavelengths around 650 nm and has a small wavelength dependence [19], the curves are almost identical. In figure 3 the experimental results for four different polarization angles χ are shown. The lines are the calculated gain curves from figure 2 for polarization angles of 0◦ and 90◦ and an electric field of 15 V/cm which corresponds to a displacement of 2.5 mm of the centers of the beams. The agreement between our experimental data and the theoretical model is good. However, from our results it is clear that both the statistics and the bandwidth have to be improved in order to reveal if the gain is polarization dependent as our theoretical model predicts.


5.

243

Conclusions

In this paper we have shown results from electron–ion collisions at very low energies, measured at CRYRING. A systematic increase of the enhancement of spontaneous recombination rates with the ionic charge over theoretical RR predictions was found. The enhancement ranges from being very small (not observable) for D+ to about a factor of 3 for Si14+ . The experimental gain curves obtained in the LIR experiment with a displaced electron beam were well reproduced by a very simple model, however, the polarization dependence predicted by this model could not be observed owing to the broad bandwidth of the laser used. References [1] H.P. Summers and W.J. Dickson, Applications of Recombination, NATO ASI Series B, Physics (Plenum Press, New York, 1992). [2] K.P. Kirby, Phys. Scripta 59 (1995) 59. [3] A. Müller, S. Schennach, M. Wagner, J. Haselbauer, O. Uwira, W. Spies, E. Jennewein, R. Becker, M. Kleinod, U. Pröbstel, N. Angert, J. Klabunde, P.H. Mokler, P. Spädtke and B. Wolf, Phys. Scripta 37 (1991) 62. [4] A. Wolf, J. Berger, M. Bock, D. Habs, B. Hochadel, G. Kilgus, G. Neureither, U. Schramm, D. Schwalm, E. Szmola, A. Müller, M. Wagner and R. Schuch, Z. Phys. D 21 (1991) S69. [5] Y. Hahn and P. Krstic, J. Phys. B: At. Mol. Opt. Phys. 27 (1994) L509. [6] Y. Hahn and J. Li, Z. Phys. D 36 (1996) 85. [7] M. Pajek and R. Schuch, Hyperfine Interact. 108 (1997) 185. [8] G. Zwicknagel, C. Toepffer and P.G. Reinhard, Hyperfine Interact. 99 (1996) 285. [9] H. Gao, D.R. DeWitt, R. Schuch, W. Zong, S. Asp and M. Pajek, Phys. Rev. Lett. 75 (1995) 4381. [10] H. Gao, S. Asp, C. Biedermann, D.R. DeWitt, R. Schuch, W. Zong and H. Danared, Hyperfine Interact. 99 (1996) 301. [11] U. Schramm, T. Schüssler, D. Habs, D. Schwalm and A. Wolf, Hyperfine Interact. 99 (1996) 309. [12] X.-W. Liu, P.J. Storey, M.J. Barlow and R.E.S. Clegg, Monthly Notices Roy. Astronom. Soc. 272 (1995) 369. [13] S. Baird, J. Bosser, C. Carli, M. Chanel, P. Lefèvre, R. Ley, R. Maccaferri, S. Maury, I. Meshkov, D. Möhl, G. Molinari, F. Motsch, H. Mulder, G. Tranquille and F. Varenne, Phys. Lett. B 361 (1995) 184. [14] H. Gao, R. Schuch, W. Zong, E. Justiniano, D.R. DeWitt, H. Lebius and W. Spies, J. Phys. B 30 (1997) L499. [15] D.J. McLaughlin and Y. Hahn, Phys. Rev. A 43 (1991) 1313. [16] U. Schramm, J. Berger, M. Grieser, D. Habs, E. Jaeschke, G. Kilgus, D. Schwalm, A. Wolf, R. Neumann and R. Schuch, Phys. Rev. Lett. 67 (1991) 22. [17] U. Schramm, T. Schüssler, D. Habs, D. Schwalm and A. Wolf, Hyperfine Interact. 99 (1996) 309. [18] S. Asp, R. Schuch, D.R. DeWitt, C. Biedermann, H. Gao, W. Zong, G. Andler and E. Justiniano, Nucl. Instrum. Methods B 117 (1996) 31. [19] E. Justiniano, G. Andler, S. Asp, D.R. DeWitt and R. Schuch, Hyperfine Interact. 108 (1997) 283. [20] S. Schennach, A. Müller, O. Uwira, J. Haselbauer, W. Spies, A. Frank, M. Wagner, R. Becker, M. Kleinod, E. Jennewein, N. Angert, P.H. Mokler, N.R. Badnell and M.S. Pindzola, Z. Phys. D 30 (1994) 291. [21] L.H. Andersen, J. Bolko and P. Kvistgaard, Phys. Rev. Lett. 64 (1990) 729; L.H. Andersen and J. Bolko, Phys. Rev. A 42 (1990) 1184.