- Email: [email protected]
Kα-Satellite spectroscopy as a tool of temperature diagnostics at KALIF
Nuclear Instruments and Methods in Physics Research A 415 (1998) 576—580
K -Satellite spectroscopy as a tool of temperature diagnostics a at KALIF B. Goel!,*, N.K. Gupta!, W. Ho¨bel!, H. Marten!, J.J. MacFarlane", P. Wang" ! Forschungszentrum Karlsruhe GmbH, Institut fu( r Neutronenphysik und Reaktortechnik, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany " Fusion Technology Institute, University of Wisconsin, Madison, USA
Abstract Interaction of the KALIF beam with thin targets produces dense plasmas in the temperature range of a few tens of eV. The Ka-satellite spectroscopy can be used to determine the temperature of such plasmas. These satellites are blue shifted. The shift is strongest for vacancies in L-shells. At temperatures typical of KALIF produced plasmas the average degree of ionisation is of the order of 4—5. Thus the diagnostic material should have only a few electrons in M-shells. In this paper we calculate spectra for Na, Mg, Al and Si with an aim to find the most suited material for temperature diagnostics under conditions typical of plasmas produced by the interaction of a KALIF beam. ( 1998 Elsevier Science B.V. All rights reserved.
1. Introduction About 20 years ago the method of K -satellite a spectroscopy was proposed by Nardi and Zinamon [1] to measure plasma temperatures. Nowadays this is successfully used to characterise high-energy density plasmas created by the interaction of intense laser or ion beams and those created by Z-pinches. In ion beam plasmas the temperatures reached so far are of the order of a few to several tens of eV. In plasmas created by intense ion beams K-shell electrons are removed by the direct impact of beam particles. As the K-shell vacancies are filled
* Corresponding author. Address for correspondence: Schanzle Strasse 5, 76187 Karlsruhe, Germany.
by outer shell electrons, lines are emitted on the long wavelength side of He -lines. For ions with a a partially filled L-shell, K -satellite lines appear a with a detectable shift towards shorter wavelengths. This shift increases as the number of L-shell electrons decreases. Because inner shell processes are inherent to light ion interaction with target atoms K -satellite spectroscopy is an obvious tool to diaga nose target plasma conditions. To be able to resolve satellite lines the target atoms need to have vacancies in L-shells at conditions prevalent in the experiment. At low plasma temperatures of a few tens of eV, as are generated by the interaction of KALIF beam, this technique can be applied to elements which have no or only a few electrons in the M-shell. In this paper we calculate the spectra emitted by different materials at the temperatures
0168-9002/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 3 7 9 - 9
B. Goel et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 576—580
577
Fig. 1. Emission spectra from Sodium, Magnesium, Aluminum and Silicon. The ion density is 1019 cm~3 and temperatures are 5, 10, 15 and 20 eV.
expected in a plasma generated with the proton beams from KALIF with a possible peak power density of 1 TW/cm2. The mean degree of ionisation of the target plasma is less than 5. That is, if we have an element with 5 or more electrons in M-shell the chances of producing holes in L-shell by thermal collision are rather dim. This limits our choice of possible heaviest material to Si that has 4 electrons in M-shell. Of course lower Z-materials with more possible number of vacancies in L-shell are favourable. However, with lowering of target Z the wavelength of the K -transition increases. Increasa ing the wavelength decreases the detector efficiency
to an extent that no detectable spectrum can be registered. For example in experiments with KALIF beam emission spectra could be measured for Mg, Al and Si but not for Na [2]. In the present paper we calculate emission spectra from Na (wavelength from 11 to 12 A_ ), Mg (wavelength from 9 to 10 A_ ), Al (wavelength from 8 to 8.4 A_ ) and Si (wavelength from 6.9 to 7.15 A_ ). After describing the calculational procedure briefly in Section 2, we will first present spectra for a uniform plasmas with ion densities of 1019 cm~3 and temperatures up to 20 eV to check the temperature sensitivity of different materials. Then we calculate spectra that are
578
B. Goel et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 576—580
Fig. 2. Emission spectra from Sodium, Magnesium, Aluminum and Silicon for a 2 lm target irradiated with protons from an applied B diode with different peak power densities.
produced in thin targets by the proton beams from KALIF.
2. Method of calculations Calculations are performed in two steps. In the first step the interaction of the KALIF proton
beam as produced by an applied B diode on a thin 2 lm target of Na, Mg, Al or Si is calculated with the radiation hydrodynamic code KATACO [3]. So obtained temperature and density profiles for different times are then fed into a Non-LTE radiation transport code NLTERT [4] to calculate time dependent emission and absorption spectra. The emission spectra are then integrated over the
B. Goel et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 576—580
whole KALIF pulse and broadened to account for the experimental resolution of j/*j of 500. These spectra can be compared with the experimental spectrum to obtain information on the temperature generated by the KALIF proton beam in the target [2]. Since there is some uncertainty in the peak power density at the target we repeat calculations by reducing the beam power by 2 and 1. Apart from 3 3 thermal ionisation it is also possible that L-shell vacancies are produced by beam impact. At the temperatures considered here the effect of such multiple ionisations is very small. Nevertheless, in the calculations this effect has been taken into account.
3. Results and discussion Fig. 1 shows calculated spectra for Na, Mg, Al, and Si plasmas with ion densities of 1019 cm~3 for temperatures of 5, 10, 15 and 20 eV. The 5 eV spectrum for Si, Al and Mg shows a strong peak which corresponds to ionisation of M-shell electrons. These are 4 in case of Si, 3 for Al and 2 for Mg. The mean degree of ionisation for all these elements is between 1.5 and 3. This peak cannot be resolved even if the resolution is increased. Na having only 1 M-shell electron shows a more structured spectrum even at these low temperatures. The mean degree of ionisation calculated for Na at 5 eV is 1.68. The fractional presence of ionisation stages 1—4 are: 0.0012, 0.362, 0.6692 and 0.0034, respectively. Thus in this case some of the L-shell electrons are removed and the spectrum shows a temperature sensitive and resolvable structure. For higher Z-elements the spectra are less structured because of less number of vacancies in L-shell. In real experiments the situation is not so simple. The plasma temperature is in general not uniform and increases with the duration of irradiation. Thus the measured spectrum is a combination of spectra emitted at different times during the beam pulse. In Fig. 2 we show, as an e.g., spectra calculated for the four materials irradiated with a proton beam from an applied B diode [5] with an assumed peak power of 1, 2 and 1 TW/cm2. The temporal beam 3 3 profile is the same in all three cases. It is seen that the spectrum is sensitive to beam power and with it
579
to temperature. Maximum temperatures achieved with these powers are of the order of 37, 32 and 27 eV respectively. To get more insight in the observed spectrum we also plot Al spectra emitted under action of the proton beam at different times in Fig. 3. During the first 20 ns the target is heated only up to 8 eV. K -lines emitted are those due to a fluorine and oxygen like ions. Later, at 30 and 40 ns nitrogen and carbon like lines are emitted. The temperature by now has gone up to 20 eV. The B-like line appears at 50 ns. The maximum temperature of 37 eV is reached at 70 ns. But by this time the proton energy has gone down to below 500 keV so that due to reduced cross sections of the proton impact ionisation there is not much intensity in lines with higher ionisation. (Note that the ordinate scale is not the same in the three plots of Fig. 3.) Therefore, in experiments with a beam power larger than 0.7 TW/cm2 and with a resolution of about 500, nitrogen and carbon like satellites will be observed indicating a maximum temperature around 20 eV. Boron and higher ionisation states will not show up due to reduced proton impact ionisation cross-sections. Peaks corresponding to temperatures of 25 eV and above, which are present in plasma created by these beams, will be observed only with improved detector efficiency.
Fig. 3. Emission spectra of Aluminum for different times irradiated with a 1 TW/cm2 proton beam.
580
B. Goel et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 576—580
In summary we have shown that K -satellite a spectroscopy is suitable to characterise a plasma generated by the interaction of a KALIF beam even at the moderate resolution of 500. However, such plasma has to be doped with elements mentioned above. The accuracy of measurement depends on the detector efficiency and resolution. We have not discussed in this paper absorption spectroscopy which can provide information at different times.
References [1] E. Nardi, Z. Zinamon, J. Appl. Phys. 52 (1981) 7075. [2] G. Meisel et al., Nucl. Instr. and Meth. A 415 (1998) 594.
[3] B. Goel, W. Ho¨bel, H. Wu¨rz, Numerical Simulation of Radiation Transport on Supercomputers, in: H. Ku¨sters (Ed.), Proc. Joint Int. Conf. vol. 2, on Mathematical Methods and Supercomputing in Nuclear Application, Karlsruhe, 19—23 April, 1993, p. 63. [4] J.J. MacFarlane, NLTERT — A code for computing radiative properties of non-LTE plasmas, Fusion Power Associates Report, FPA-93-6, Madison, 1993. [5] H. Bluhm et al., Stability and operating characteristics of the applied B proton extraction diode on KALIF, in: Proc. of the 10th Int. Conf. on High-Power Particle Beams, San Diego, CA, 20—24 June, 1994, NTIS, Springfield, VA, 1995, pp. 77—82.
K -Satellite spectroscopy as a tool of temperature diagnostics a at KALIF B. Goel!,*, N.K. Gupta!, W. Ho¨bel!, H. Marten!, J.J. MacFarlane", P. Wang" ! Forschungszentrum Karlsruhe GmbH, Institut fu( r Neutronenphysik und Reaktortechnik, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany " Fusion Technology Institute, University of Wisconsin, Madison, USA
Abstract Interaction of the KALIF beam with thin targets produces dense plasmas in the temperature range of a few tens of eV. The Ka-satellite spectroscopy can be used to determine the temperature of such plasmas. These satellites are blue shifted. The shift is strongest for vacancies in L-shells. At temperatures typical of KALIF produced plasmas the average degree of ionisation is of the order of 4—5. Thus the diagnostic material should have only a few electrons in M-shells. In this paper we calculate spectra for Na, Mg, Al and Si with an aim to find the most suited material for temperature diagnostics under conditions typical of plasmas produced by the interaction of a KALIF beam. ( 1998 Elsevier Science B.V. All rights reserved.
1. Introduction About 20 years ago the method of K -satellite a spectroscopy was proposed by Nardi and Zinamon [1] to measure plasma temperatures. Nowadays this is successfully used to characterise high-energy density plasmas created by the interaction of intense laser or ion beams and those created by Z-pinches. In ion beam plasmas the temperatures reached so far are of the order of a few to several tens of eV. In plasmas created by intense ion beams K-shell electrons are removed by the direct impact of beam particles. As the K-shell vacancies are filled
* Corresponding author. Address for correspondence: Schanzle Strasse 5, 76187 Karlsruhe, Germany.
by outer shell electrons, lines are emitted on the long wavelength side of He -lines. For ions with a a partially filled L-shell, K -satellite lines appear a with a detectable shift towards shorter wavelengths. This shift increases as the number of L-shell electrons decreases. Because inner shell processes are inherent to light ion interaction with target atoms K -satellite spectroscopy is an obvious tool to diaga nose target plasma conditions. To be able to resolve satellite lines the target atoms need to have vacancies in L-shells at conditions prevalent in the experiment. At low plasma temperatures of a few tens of eV, as are generated by the interaction of KALIF beam, this technique can be applied to elements which have no or only a few electrons in the M-shell. In this paper we calculate the spectra emitted by different materials at the temperatures
0168-9002/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 3 7 9 - 9
B. Goel et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 576—580
577
Fig. 1. Emission spectra from Sodium, Magnesium, Aluminum and Silicon. The ion density is 1019 cm~3 and temperatures are 5, 10, 15 and 20 eV.
expected in a plasma generated with the proton beams from KALIF with a possible peak power density of 1 TW/cm2. The mean degree of ionisation of the target plasma is less than 5. That is, if we have an element with 5 or more electrons in M-shell the chances of producing holes in L-shell by thermal collision are rather dim. This limits our choice of possible heaviest material to Si that has 4 electrons in M-shell. Of course lower Z-materials with more possible number of vacancies in L-shell are favourable. However, with lowering of target Z the wavelength of the K -transition increases. Increasa ing the wavelength decreases the detector efficiency
to an extent that no detectable spectrum can be registered. For example in experiments with KALIF beam emission spectra could be measured for Mg, Al and Si but not for Na [2]. In the present paper we calculate emission spectra from Na (wavelength from 11 to 12 A_ ), Mg (wavelength from 9 to 10 A_ ), Al (wavelength from 8 to 8.4 A_ ) and Si (wavelength from 6.9 to 7.15 A_ ). After describing the calculational procedure briefly in Section 2, we will first present spectra for a uniform plasmas with ion densities of 1019 cm~3 and temperatures up to 20 eV to check the temperature sensitivity of different materials. Then we calculate spectra that are
578
B. Goel et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 576—580
Fig. 2. Emission spectra from Sodium, Magnesium, Aluminum and Silicon for a 2 lm target irradiated with protons from an applied B diode with different peak power densities.
produced in thin targets by the proton beams from KALIF.
2. Method of calculations Calculations are performed in two steps. In the first step the interaction of the KALIF proton
beam as produced by an applied B diode on a thin 2 lm target of Na, Mg, Al or Si is calculated with the radiation hydrodynamic code KATACO [3]. So obtained temperature and density profiles for different times are then fed into a Non-LTE radiation transport code NLTERT [4] to calculate time dependent emission and absorption spectra. The emission spectra are then integrated over the
B. Goel et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 576—580
whole KALIF pulse and broadened to account for the experimental resolution of j/*j of 500. These spectra can be compared with the experimental spectrum to obtain information on the temperature generated by the KALIF proton beam in the target [2]. Since there is some uncertainty in the peak power density at the target we repeat calculations by reducing the beam power by 2 and 1. Apart from 3 3 thermal ionisation it is also possible that L-shell vacancies are produced by beam impact. At the temperatures considered here the effect of such multiple ionisations is very small. Nevertheless, in the calculations this effect has been taken into account.
3. Results and discussion Fig. 1 shows calculated spectra for Na, Mg, Al, and Si plasmas with ion densities of 1019 cm~3 for temperatures of 5, 10, 15 and 20 eV. The 5 eV spectrum for Si, Al and Mg shows a strong peak which corresponds to ionisation of M-shell electrons. These are 4 in case of Si, 3 for Al and 2 for Mg. The mean degree of ionisation for all these elements is between 1.5 and 3. This peak cannot be resolved even if the resolution is increased. Na having only 1 M-shell electron shows a more structured spectrum even at these low temperatures. The mean degree of ionisation calculated for Na at 5 eV is 1.68. The fractional presence of ionisation stages 1—4 are: 0.0012, 0.362, 0.6692 and 0.0034, respectively. Thus in this case some of the L-shell electrons are removed and the spectrum shows a temperature sensitive and resolvable structure. For higher Z-elements the spectra are less structured because of less number of vacancies in L-shell. In real experiments the situation is not so simple. The plasma temperature is in general not uniform and increases with the duration of irradiation. Thus the measured spectrum is a combination of spectra emitted at different times during the beam pulse. In Fig. 2 we show, as an e.g., spectra calculated for the four materials irradiated with a proton beam from an applied B diode [5] with an assumed peak power of 1, 2 and 1 TW/cm2. The temporal beam 3 3 profile is the same in all three cases. It is seen that the spectrum is sensitive to beam power and with it
579
to temperature. Maximum temperatures achieved with these powers are of the order of 37, 32 and 27 eV respectively. To get more insight in the observed spectrum we also plot Al spectra emitted under action of the proton beam at different times in Fig. 3. During the first 20 ns the target is heated only up to 8 eV. K -lines emitted are those due to a fluorine and oxygen like ions. Later, at 30 and 40 ns nitrogen and carbon like lines are emitted. The temperature by now has gone up to 20 eV. The B-like line appears at 50 ns. The maximum temperature of 37 eV is reached at 70 ns. But by this time the proton energy has gone down to below 500 keV so that due to reduced cross sections of the proton impact ionisation there is not much intensity in lines with higher ionisation. (Note that the ordinate scale is not the same in the three plots of Fig. 3.) Therefore, in experiments with a beam power larger than 0.7 TW/cm2 and with a resolution of about 500, nitrogen and carbon like satellites will be observed indicating a maximum temperature around 20 eV. Boron and higher ionisation states will not show up due to reduced proton impact ionisation cross-sections. Peaks corresponding to temperatures of 25 eV and above, which are present in plasma created by these beams, will be observed only with improved detector efficiency.
Fig. 3. Emission spectra of Aluminum for different times irradiated with a 1 TW/cm2 proton beam.
580
B. Goel et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 576—580
In summary we have shown that K -satellite a spectroscopy is suitable to characterise a plasma generated by the interaction of a KALIF beam even at the moderate resolution of 500. However, such plasma has to be doped with elements mentioned above. The accuracy of measurement depends on the detector efficiency and resolution. We have not discussed in this paper absorption spectroscopy which can provide information at different times.
References [1] E. Nardi, Z. Zinamon, J. Appl. Phys. 52 (1981) 7075. [2] G. Meisel et al., Nucl. Instr. and Meth. A 415 (1998) 594.
[3] B. Goel, W. Ho¨bel, H. Wu¨rz, Numerical Simulation of Radiation Transport on Supercomputers, in: H. Ku¨sters (Ed.), Proc. Joint Int. Conf. vol. 2, on Mathematical Methods and Supercomputing in Nuclear Application, Karlsruhe, 19—23 April, 1993, p. 63. [4] J.J. MacFarlane, NLTERT — A code for computing radiative properties of non-LTE plasmas, Fusion Power Associates Report, FPA-93-6, Madison, 1993. [5] H. Bluhm et al., Stability and operating characteristics of the applied B proton extraction diode on KALIF, in: Proc. of the 10th Int. Conf. on High-Power Particle Beams, San Diego, CA, 20—24 June, 1994, NTIS, Springfield, VA, 1995, pp. 77—82.