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Experimental analysis of the stopping cross sections and of the charge changing processes for Clq+ projectiles at the maximum of the stopping power
Nuclear Instruments and Methods in Physics Research A 464 (2001) 253–256
Experimental analysis of the stopping cross sections and of the charge changing processes for Clq+ projectiles at the maximum of the stopping power D. Gard"esa,*, M. Chabota, M. Nectouxa, G. Maynardb, C. Deutschb, G. Belyaevc a
! Institut de Physique Nucleaire (CNRS - IN2P3), Universite! Paris XI, B.P. 1, F-91406 Orsay, Cedex, France b Laboratoire de Physique des Gaz et des Plasmas, Universite! Paris XI, F-91406 Orsay, France c Institute of Theoretical and Experimental Physics, ITEP Moscow, Russia
Abstract Chlorine 7+ ions interacting with different states of matter are compared in the framework of an accurate experimental measurement of energy loss as a function of the exiting charge state. # 2001 Published by Elsevier Science B.V. PACS: 34.50Bw; 52.40.Mj; 52.58.Hm Keywords: Energy loss; Heavy ions; Charge exchange; Energy straggling; Inertial confinement fusion (ICF)
1. Introduction An extensive analysis of the energy lost by chlorine ions interacting with a deuterium target has been initiated some years ago in the framework of both ion–plasma and ion–gas interaction experiments [1]. Dynamic rate of charge exchange processes is strongly dependent on the stopping medium (solid, gas or plasma). The gas target experiments realized with an accuracy of a few percent on relative charge state stopping power are on the basis of an elaborate comparison with theory [2,3]. The plasma experiments enlarge these effects and provide a new insight on the X-ray
conversion processes involved in ion confinement fusion scenarios. The system Cl+D2 has been chosen in order to enhance the charge state dependency of the stopping power. With such a low Z target we are able to observe a meaningful dynamical effect due to charge exchange rate. The incident energy of 1.5 MeV/amu corresponds to the maximum of stopping power, and the target is thin enough for neglecting multiple-collision processes. A direct relevance to ICF of these observations, concerns the energy straggling and the ensuing consequence on energy deposition profile.
2. Experimental set-up *Corresponding author. Tel.: +33-16915-7217; fax: +3316915-4507. E-mail address: [email protected] (D. Garde`s).
The measurements are very demanding from the experimental point of view. The windowless gas
0168-9002/01/$ - see front matter # 2001 Published by Elsevier Science B.V. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 0 0 4 4 - 4
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and plasma targets have been especially designed for this purpose. The experimental set-up has been described in an earlier paper [1]. A special attention has been paid to the control of the interfaces between the target and the vacuum and also to the remaining impurities inside the target. Analysis of the charge state distribution is achieved in a large acceptance magnetic spectrometer ( 2 mrad; dE/E =2 104). The ‘‘splitpole magnet’’ is a special device [4] which allows to refocus entrance trajectories within a wide angular acceptance. This is particularly useful for the plasma experiments where the well known ‘‘plasma lens effect’’ is a source of intense perturbations for the exiting trajectories. The focal plane of the spectrometer is equipped with a 1 m long, fast plastic scintillator. The light emitted under the impact of ions is collected via an intensified CCD camera and digitized in a PC computer. The energy loss of a given charge state induces a small displacement in the focal plane. A calibration between these displacements and the incident energy was performed by varying the
beam energy delivered by the machine. In this case the accuracy of the absolute energy determination is of the order of 104. 3. Stopping power results The energy loss for chlorine ions in cold gas and plasma are presented in Figs. 1 and 2. The cold gas results were obtained by varying progressively the gas pressure inside the target. The absolute pressure is measured before the opening of the fast valves. A corrective factor is applied to the initial pressure in order to take into account the leakage during the measurement [1]. The target thickness uncertainty is 3%. The plasma is generated by an electrical discharge inside 10 Torr of deuterium. The energy loss behavior reflects the density evolution in the target during the discharge. The error on the plasma thickness is 10%. Eleven ms after the ignition, the free electron linear density reaches a maximum value of 1.35 1019 e/cm [1]. The results in cold gas and plasma targets have been compared for this linear density.
Fig. 1. Energy loss as a function outgoing charge state for the system Cl7++D2, cold gas.
D. Garde`s et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 253–256
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Fig. 3. Schematic drawing of the charge exchange process as a function of linear density.
Fig. 2. Energy loss as a function outgoing charge state for the system Cl7++D2, plasma.
4. General behavior Cold gas and plasma experiments have been performed with a chlorine 7+ at the entrance of the target. This initial charge state is far from the equilibrium value, Qeq =13.5 in the cold gas. The Fig. 3 presents a schematic evolution of the charge state during the travel through the cold target. Three main parts can be distinguished: in the first one, labeled (1) on the graph, the incident ion reaches gradually its equilibrium charge state Qeq . During the second part the projectile charge oscillates around Qeq . In these experiments Qeq is nearly constant because the projectile velocity does not change drastically along the interaction path. The last charge transfer before leaving the target delimits the third part of Fig. 3. This is the typical behavior obtained for gas target linear density of the order of several 1019 e/cm. Considering these three parts, the last path length is crucial in deciding to explain the energy loss difference at the output of the target. Taking the final stopping power, as a first approximation, proportional to Qexit , then the last path length determines the observed difference in the energy lost by two successive Qexit . This behavior is reproduced by a stochastic simulation, introducing in a Monte-
Carlo code the complete set of charge changing cross sections already determined in preceding experiments [5,6]. The comparison between cold gas and plasma at the same linear density is presented in Fig. 4, where the energy loss of four exiting charge states is reported. A graph corresponding to a solid target (carbon) has been added to complete the general comparison. In this particular case, the absolute value of the energy loss has no particular interest, but the ratio between two charge state energy losses is relevant to our discussion. The mean free path relative to a given charge state is inversely proportional to the total charge changing cross-section. In a carbon foil, this corresponds to a very short length and the effect on the differential stopping dE=dQ DE=DQ is rather small. In the cold gas in our particular case, dE=dQ is about 50 keV. The highest slope of the energy loss is obtained in the plasma target. One part of this high slope in plasma is due to the enhanced plasma stopping and the second part to a reduction of the total charge changing cross sections due to the suppression of capture channels [1]. We see here that the differential stopping dE=dQ provided an additional demonstration of the enhanced properties in the interaction process exhibited by a plasma target beside the well documented enhanced stopping and stripping capacities, a fully ionized target yields also an increased differential stopping between the exiting ions. VII. POSTER SESSION A
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on the ‘‘characteristic thickness’’ Rc ¼ 1=s (where s is the charge changing cross-section) that we can associate to a given charge state transition. If the linear density ne l is small relatively to Rc , this effect becomes dominant in the straggling process. The ratio ne l=Rc will increase if one considers a heavier projectile in a thick target as it is the case for the 10 GeV Bi beam in the ICF converter. In this case, not only the energy deposition profile will depends on the initial charge state distribution, but also the straggling induced by the charge changing processes can be large enough to strongly modify the form of the final Bragg peak [6,7].
6. Conclusion We have presented a complete set of experimental data which provides a new insight on the origin of the energy straggling in the heavy ions interaction with light materials. The differential stopping power resulting from charge exchange processes is particularly crucial when the charge changing rate is reduced like in plasma, introducing a strong gradient of energy loss as a function of the incoming and outgoing charge distribution. These results are also on the basis of an extensive discussion concerning the comparison with the CKLT stopping theory [3,7]. Fig. 4. Comparison of the energy loss for carbon, cold deuterium and deuterium plasma as a function of the outgoing charge state.
5. Consequences on straggling The charge changing processes can affect the energy deposited in plasma in different ways, depending on the target thickness. For a thin target the large values of dE=dQ observed in plasma, introduced a stronger dependency, as compared to the neutral case, of the energy lost on the initial and final charge state distributions of the heavy ions beam. In particular, an entrance window will change the deposited energy in the plasma. The relative importance of the contribution of dE=dQ on this deposited energy depends
References [1] M. Chabot, M. Nectoux, D. Gard"es, G. Maynard, C. Deutsch, Nucl. Instr. and Meth. A 415 (1998) 571. [2] G. Maynard, K. Katsonis, G. Zwicknagel, S. Mabong, M. Chabot, D. Gard"es, Yu.K. Kurilenkov, Nucl. Instr. and Meth. A 415 (1998) 687. [3] M. Chabot et al., to be submitted. [4] J.E. Spencer, H.A. Enge, Nucl. Instr. and Meth. A 49 (1967) 181. [5] M. Chabot, D. Gard"es, P. Box, J. Kiener, C. Deutsch, G. Maynard, V. Andr!e, C. Fleurier, D. Hong, K. Woher, Phys. Rev. E 51 (4) (1995) 3504. [6] C. Labaure, W.J. Hogan, K.A. Tanka (Eds.), Inertial Fusion Science and Applications, 1999, Elsevier Science B.V., Amsterdam. 2000. [7] G. Maynard et al., Nucl. Instr and Meth. A 464 (2001) 86, these proceedings.
Experimental analysis of the stopping cross sections and of the charge changing processes for Clq+ projectiles at the maximum of the stopping power D. Gard"esa,*, M. Chabota, M. Nectouxa, G. Maynardb, C. Deutschb, G. Belyaevc a
! Institut de Physique Nucleaire (CNRS - IN2P3), Universite! Paris XI, B.P. 1, F-91406 Orsay, Cedex, France b Laboratoire de Physique des Gaz et des Plasmas, Universite! Paris XI, F-91406 Orsay, France c Institute of Theoretical and Experimental Physics, ITEP Moscow, Russia
Abstract Chlorine 7+ ions interacting with different states of matter are compared in the framework of an accurate experimental measurement of energy loss as a function of the exiting charge state. # 2001 Published by Elsevier Science B.V. PACS: 34.50Bw; 52.40.Mj; 52.58.Hm Keywords: Energy loss; Heavy ions; Charge exchange; Energy straggling; Inertial confinement fusion (ICF)
1. Introduction An extensive analysis of the energy lost by chlorine ions interacting with a deuterium target has been initiated some years ago in the framework of both ion–plasma and ion–gas interaction experiments [1]. Dynamic rate of charge exchange processes is strongly dependent on the stopping medium (solid, gas or plasma). The gas target experiments realized with an accuracy of a few percent on relative charge state stopping power are on the basis of an elaborate comparison with theory [2,3]. The plasma experiments enlarge these effects and provide a new insight on the X-ray
conversion processes involved in ion confinement fusion scenarios. The system Cl+D2 has been chosen in order to enhance the charge state dependency of the stopping power. With such a low Z target we are able to observe a meaningful dynamical effect due to charge exchange rate. The incident energy of 1.5 MeV/amu corresponds to the maximum of stopping power, and the target is thin enough for neglecting multiple-collision processes. A direct relevance to ICF of these observations, concerns the energy straggling and the ensuing consequence on energy deposition profile.
2. Experimental set-up *Corresponding author. Tel.: +33-16915-7217; fax: +3316915-4507. E-mail address: [email protected] (D. Garde`s).
The measurements are very demanding from the experimental point of view. The windowless gas
0168-9002/01/$ - see front matter # 2001 Published by Elsevier Science B.V. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 0 0 4 4 - 4
VII. POSTER SESSION A
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D. Garde`s et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 253–256
and plasma targets have been especially designed for this purpose. The experimental set-up has been described in an earlier paper [1]. A special attention has been paid to the control of the interfaces between the target and the vacuum and also to the remaining impurities inside the target. Analysis of the charge state distribution is achieved in a large acceptance magnetic spectrometer ( 2 mrad; dE/E =2 104). The ‘‘splitpole magnet’’ is a special device [4] which allows to refocus entrance trajectories within a wide angular acceptance. This is particularly useful for the plasma experiments where the well known ‘‘plasma lens effect’’ is a source of intense perturbations for the exiting trajectories. The focal plane of the spectrometer is equipped with a 1 m long, fast plastic scintillator. The light emitted under the impact of ions is collected via an intensified CCD camera and digitized in a PC computer. The energy loss of a given charge state induces a small displacement in the focal plane. A calibration between these displacements and the incident energy was performed by varying the
beam energy delivered by the machine. In this case the accuracy of the absolute energy determination is of the order of 104. 3. Stopping power results The energy loss for chlorine ions in cold gas and plasma are presented in Figs. 1 and 2. The cold gas results were obtained by varying progressively the gas pressure inside the target. The absolute pressure is measured before the opening of the fast valves. A corrective factor is applied to the initial pressure in order to take into account the leakage during the measurement [1]. The target thickness uncertainty is 3%. The plasma is generated by an electrical discharge inside 10 Torr of deuterium. The energy loss behavior reflects the density evolution in the target during the discharge. The error on the plasma thickness is 10%. Eleven ms after the ignition, the free electron linear density reaches a maximum value of 1.35 1019 e/cm [1]. The results in cold gas and plasma targets have been compared for this linear density.
Fig. 1. Energy loss as a function outgoing charge state for the system Cl7++D2, cold gas.
D. Garde`s et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 253–256
255
Fig. 3. Schematic drawing of the charge exchange process as a function of linear density.
Fig. 2. Energy loss as a function outgoing charge state for the system Cl7++D2, plasma.
4. General behavior Cold gas and plasma experiments have been performed with a chlorine 7+ at the entrance of the target. This initial charge state is far from the equilibrium value, Qeq =13.5 in the cold gas. The Fig. 3 presents a schematic evolution of the charge state during the travel through the cold target. Three main parts can be distinguished: in the first one, labeled (1) on the graph, the incident ion reaches gradually its equilibrium charge state Qeq . During the second part the projectile charge oscillates around Qeq . In these experiments Qeq is nearly constant because the projectile velocity does not change drastically along the interaction path. The last charge transfer before leaving the target delimits the third part of Fig. 3. This is the typical behavior obtained for gas target linear density of the order of several 1019 e/cm. Considering these three parts, the last path length is crucial in deciding to explain the energy loss difference at the output of the target. Taking the final stopping power, as a first approximation, proportional to Qexit , then the last path length determines the observed difference in the energy lost by two successive Qexit . This behavior is reproduced by a stochastic simulation, introducing in a Monte-
Carlo code the complete set of charge changing cross sections already determined in preceding experiments [5,6]. The comparison between cold gas and plasma at the same linear density is presented in Fig. 4, where the energy loss of four exiting charge states is reported. A graph corresponding to a solid target (carbon) has been added to complete the general comparison. In this particular case, the absolute value of the energy loss has no particular interest, but the ratio between two charge state energy losses is relevant to our discussion. The mean free path relative to a given charge state is inversely proportional to the total charge changing cross-section. In a carbon foil, this corresponds to a very short length and the effect on the differential stopping dE=dQ DE=DQ is rather small. In the cold gas in our particular case, dE=dQ is about 50 keV. The highest slope of the energy loss is obtained in the plasma target. One part of this high slope in plasma is due to the enhanced plasma stopping and the second part to a reduction of the total charge changing cross sections due to the suppression of capture channels [1]. We see here that the differential stopping dE=dQ provided an additional demonstration of the enhanced properties in the interaction process exhibited by a plasma target beside the well documented enhanced stopping and stripping capacities, a fully ionized target yields also an increased differential stopping between the exiting ions. VII. POSTER SESSION A
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D. Garde`s et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 253–256
on the ‘‘characteristic thickness’’ Rc ¼ 1=s (where s is the charge changing cross-section) that we can associate to a given charge state transition. If the linear density ne l is small relatively to Rc , this effect becomes dominant in the straggling process. The ratio ne l=Rc will increase if one considers a heavier projectile in a thick target as it is the case for the 10 GeV Bi beam in the ICF converter. In this case, not only the energy deposition profile will depends on the initial charge state distribution, but also the straggling induced by the charge changing processes can be large enough to strongly modify the form of the final Bragg peak [6,7].
6. Conclusion We have presented a complete set of experimental data which provides a new insight on the origin of the energy straggling in the heavy ions interaction with light materials. The differential stopping power resulting from charge exchange processes is particularly crucial when the charge changing rate is reduced like in plasma, introducing a strong gradient of energy loss as a function of the incoming and outgoing charge distribution. These results are also on the basis of an extensive discussion concerning the comparison with the CKLT stopping theory [3,7]. Fig. 4. Comparison of the energy loss for carbon, cold deuterium and deuterium plasma as a function of the outgoing charge state.
5. Consequences on straggling The charge changing processes can affect the energy deposited in plasma in different ways, depending on the target thickness. For a thin target the large values of dE=dQ observed in plasma, introduced a stronger dependency, as compared to the neutral case, of the energy lost on the initial and final charge state distributions of the heavy ions beam. In particular, an entrance window will change the deposited energy in the plasma. The relative importance of the contribution of dE=dQ on this deposited energy depends
References [1] M. Chabot, M. Nectoux, D. Gard"es, G. Maynard, C. Deutsch, Nucl. Instr. and Meth. A 415 (1998) 571. [2] G. Maynard, K. Katsonis, G. Zwicknagel, S. Mabong, M. Chabot, D. Gard"es, Yu.K. Kurilenkov, Nucl. Instr. and Meth. A 415 (1998) 687. [3] M. Chabot et al., to be submitted. [4] J.E. Spencer, H.A. Enge, Nucl. Instr. and Meth. A 49 (1967) 181. [5] M. Chabot, D. Gard"es, P. Box, J. Kiener, C. Deutsch, G. Maynard, V. Andr!e, C. Fleurier, D. Hong, K. Woher, Phys. Rev. E 51 (4) (1995) 3504. [6] C. Labaure, W.J. Hogan, K.A. Tanka (Eds.), Inertial Fusion Science and Applications, 1999, Elsevier Science B.V., Amsterdam. 2000. [7] G. Maynard et al., Nucl. Instr and Meth. A 464 (2001) 86, these proceedings.