Pii: s0168-9002(01)00032-8

Nuclear Instruments and Methods in Physics Research A 464 (2001) 192–195 Magnetized cylindrical targets for heavy ion fusionq A.J. Kempa,*, M. Baskob, J. Meyer-ter-Vehna a Max-Planck-Institut f .ur Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany b Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117259 Moscow, Russia Ignition conditions for magnetized cylindrical fusion targets are investigated by means of one-dimensional hydrodynamic calculations. Of particular interest is the effect of a tamper surroundingthe fuel at the time of stagnation.
The key assumption in this paper is that the targets are magnetically insulated, i.e. electronic and ionic heat conductionas well as the diffusion of 3.5 MeV alpha particles are suppressed. It is found that magnetically insulated targets can beignited at significantly reduced values of the fuel rR, but, in contrast to conventional fusion targets, the value of the fuelrR at ignition depends on the fuel mass as well as on the tamper entropy. # 2001 Elsevier Science B.V. All rightsreserved.
Keywords: Magnetized fuel; Ignition threshold However, this would be acceptable as longas the fuel can be ignited. Once ignition is achieved, Magnetized target fusion (MTF) stands for the benefit is a significant reduction of the required inertial confinement fusion (ICF) with an addi- driver power [5], compared to the usual ICF. A tional magnetic field; it has been discussed mostly natural way to reduce energy losses out of the fuel in the context of spherically symmetric implosions is to apply an external magnetic field in the target, [1,2]. The recent interest in cylindrical configura- in axial or azimuthal direction. In particular, it has tions [3–5] arises in the context of heavy ion beam been shown [5] that ignition can be achieved at fusion, where a cylindrical geometry is the natural significantly reduced rR values if the gyroradius of choice in view of the cylindrical geometry of the the 3.5 MeV alpha particles in the magnetic field is beam. A major drawback of this geometry is that, of the same order as the fuel radius at stagnation, under similar constraints on symmetry and stabi- always on the assumption that the fuel is lity, cylindrical implosions are less efficient than spherical ones [4]. Hence they result in lower rR In this article, we therefore examine the role of the confinement for tamped fuel volumes at lowrR. We assume the fuel plasma to be magnetically insulated, which means that heat conduction losses as well as diffusion of alpha particles are sup- E-mail address: kemp@mpq.mpg.de (A.J. Kemp).
pressed alongthe radial direction. Our main 0168-9002/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 0 0 3 2 - 8 A.J. Kemp et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 192–195 conclusion is that the fuel rR necessary for the lower limit for the ignition temperature of ICF ignition depends both on the fuel mass and the targets, which is at approximately 4.5 keV [10]. We tamper entropy. Below, we present the results of have selected our workingpoint at T0 ¼ 7 keV, but one-dimensional computer simulations of pre- the final results of this paper are not selective to assembled fuel–tamper configurations. Similar the exact number. Results will be plotted as configurations have been widely studied for non- magnetized targets in a spherical geometry [6].
Here, we reconsider this matter for magnetizedcylindrical targets to assess their potential for ICF.
The simulations described below were per- 2. Basic assumptions and initial configuration formed with the Lagrangean, one-dimensionalhydrodynamics code DEIRA [8], featuringthree Since the fuel ignition occurs approximately temperatures for electrons, ions and radiation, real when the target implosion has come to a halt, one matter equation of state and opacity tables, and can, as a first step, investigate the basic properties thermonuclear reactions. Non-local deposition of of the ignition process by starting at the time of fast alpha particles in the fuel is modeled by a stagnation. Such a configuration consists of a hot diffusion equation [8,9]. In order to account for DT fuel volume surrounded by a layer of dense magnetic insulation of the target in the sense tamper material to provide inertial confinement to discussed in Section 2, the diffusion coefficient for the fuel. The tamper thickness is characterized by fast alpha particles and coefficients for both ionic the ratio xt of the outer tamper radius to the outer and electronic heat conduction are set to zero in fuel boundary at stagnation. In order to account for different heatingsituations, we vary Tt in the The role of the tamper is to provide inertial range 1–100 eV. We assume that at stagnation the confinement to the hot fuel in order to allow pressure is constant throughout the compressed considerable burn-up before the configuration core [7] and that the profiles of density and explodes. While growing tamper thickness xt temperature are uniform in fuel and tamper layer.
improves the inertial confinement, it also influ- This simplifyingassumption reproduces the main ences the efficiency of the configuration. After physical aspects of realistic targets at stagnation, reachinga maximum at approximately xt ¼ 1:8, as expected from one-dimensional simulations of the fraction of burnt fuel saturates and the efficiency drops. As an optimum workingpoint, The limit of magnetically insulated targets, as defined above, is adequate if the collision fre- In contrast to non-magnetized ICF targets, quency of alpha particles and electrons is small where one observes a marked increase of the fuel compared to the cyclotron frequency of the alpha burn fraction when the fuel rR exceeds the alpha particles in the magnetic field. The energy relaxa- stopping range of approximately 0.3 g/cm2, the tion time between alpha particles and electrons is fuel burn fraction in magnetically insulated targets not affected by the magnetic field [8,9]. Since there increases gradually with the fuel rR; this is caused is a wide range of fuel parameters where the effects by the complete redeposition of alpha particles in of magnetic field pressure on the plasma dynamics the fuel, even for low values of the fuel rR: Fig. 1 can be neglected, we can perform purely hydro- shows the peak fuel temperature reached in dynamic, rather than full MHD simulations.
various target explosions as a function of the The fuel is described in terms of its stagnation initial fuel rR. Each point in the plot represents an temperature T0, the fuel confinement parameter individual history of a target evolution with given (rR) and the fuel mass per unit length m ¼ prR2.
initial values of fuel mass m and rR; the curves Its initial temperature T0 can be chosen at any connect points of constant fuel mass. Targets are reasonable margin of about a factor 1.5–2 above called ‘‘ignited’’ if the peak fuel temperature A.J. Kemp et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 192–195 Fig. 1. Peak fuel temperature during target disintegration vs.
Fig. 2. Ignition rR vs. fuel mass for different choices of the initial fuel rR, for targets with various fuel masses m. The thickness xt and initial temperature Tt of the tamper. The ignition threshold is indicated by the horizontal line.
ignition scalings for two values of the fuel mass are indicated bydotted lines. For the shaded area, see Section 4.
duringdisintegration exceeds 21 keV, i.e. if the fueltemperature rises at least to three times the initialvalue of T0 ¼ 7 keV, correspondingto a fuel burnfraction of the order of ten percent. Here, we need such a definition since there is no clear ignition‘‘cliff’’, as in the case of the non-magnetized We have investigated ignition conditions for targets. This definition is consistent with the magnetically insulated cylindrical fusion targets by ignition threshold of non-magnetized targets.
The dependence of the rR ignition threshold on at the time of stagnation. This has been done by the fuel mass is shown explicitly in Fig. 2. Various means of one-dimensional hydrodynamic simula- curves are presented for different values of the tions, where the effects of heat conduction and the tamper parameters in order to account for diffusion of alpha particles have been ignored. We different implosion histories. The ignition thresh- have found that under these assumptions, ignition occurs only when a minimum fuel rR is reached at where 0:654k41:0, dependingon the fuel mass as stagnation. The minimum rR for fuel ignition indicated on Fig. 2. It turns out that the position depends on the fuel mass as well as on the tamper of the ignition threshold rR for large fuel masses entropy. This result can serve as a guideline m51.0 mg/cm depends on the tamper entropy.
in the vast parameter space, when designing For tampers with Tt % 100 eV, it remains above cylindrical MTF targets that should ignite in the 0.01 g/cm2. For cold tampers, however, it can drop significantly below this value. Also shown in Fig. 2 is the dependence on the tamper thickness xt. The heavy ion beams is indicated by the shaded area in ignition rR of targets with a thin (xt ¼ 1:4) and Fig. 2. The boundaries have been selected such those with a large ðxt ¼ 1:7) tamper differs by that the lowest possible ðrRÞign is obtained at fuel about a factor of two. The simulation results energies of a few MJ/cm, which may be available presented above can be understood in terms of from future heavy ion drivers. The window equation of state properties of the tamper. This corresponds to fuel radii up to 1 mm and pressures below 10 Gbar. Compared to non-magnetized ICF A.J. Kemp et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 192–195 targets, magnetic insulation of cylindrical DT targets allows to reduce the ignition rR thresholdby a factor of 10–30, dependingon the implosion [1] I. Lindemuth, R. Kirkpatrick, 23 (1983) 263.
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[3] M. Churazov, B. Sharkov, E. Zabrodina, 32 (1996) 577.
breakeven in cylindrical ICF targets scales as [5] [4] M. Basko, CEA Report EUR-CEA-FC-1645, 1998.
Pdr / ðrRÞ2 , this leads to a significant reduction [5] M. Basko, A. Kemp, J. Meyer-ter-Vehn, Nuclear Fusion in the required driver power for heavy ion beam driven, magnetized cylindrical targets in the MTF [6] S. Atzeni, Jpn. J. Appl. Phys. 34 (1995) 1980.
[7] J. Meyer-ter-Vehn, Nuclear Fusion 22 (1982) 561.
[8] M. Basko, DEIRA-3. 1-D 3-T Hydrodynamic Code for In this paper, we have not considered how the assembled fuel–tamper configurations can be reached by target implosions. Neither have we [9] M. Liberman, A. Velikovich, J. Plasma Phys. 31 (1984) considered losses through the ends of the cylind- rical configuration, see [5], nor the questions of [10] J. Lindl, in: A. Caruso, E. Sindoni (Eds.), International School of Plasma Physics Piero Caldirola: Inertial Con- symmetry and stability. These questions, together with a more realistic implementation of the [11] A. Kemp, M. Basko, J. Meyer-ter-Vehn, Ignition condi- magnetic field, will have to be addressed in future tion for magnetically insulated tampered ICF targets . . .,

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