Heavy ion fusion targets; issues for fast ignition

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Abstract

During the last 36 years researchers have suggested and evaluated a large number of target designs for heavy ion inertial fusion. The different target designs can be classified according to their mode of ignition, their method of implosion, and their size. Ignition modes include hot-spot ignition and fast ignition. Methods of implosion include direct drive and indirect drive. Historically there has been significant work on indirectly driven targets with hot-spot ignition. Recently there has been increasing interest in directly driven targets with ion driven fast ignition. In principle, fast ignition might lead to improved target performance. On the other hand, fast ignition imposes stringent requirements on accelerators and beam physics. Furthermore, fast ignition magnifies the importance of a number of traditional target physics issues associated with ion beam energy deposition and fuel preheat. This paper will discuss the advantages and disadvantages of the various classes of targets. It will also discuss some issues that must be resolved to assess the feasibility of ion fast ignition.

Introduction

Since the first international workshop on heavy ion fusion in 1976, there has been a large proliferation of target designs—far too many to cover in a single paper. Some system of classification is needed. In this paper, we find it convenient to classify targets according to their mode of ignition, their method of implosion, and their size. Volume ignition, hot-spot ignition, shock ignition, and fast ignition are modes of ignition. Direct drive and indirect drive are methods of implosion; but, unlike laser targets where there is a sharp distinction between direct drive and indirect drive, ion targets exhibit a continuum between the two extremes. Using this classification system, a given target design can be described by a point in the 3-dimensional space shown in Fig. 1.

Different regions in this 3-dimensional space have different characteristics. Consider the vertical axis, the ignition mode. It requires ∼109 J/g to heat deuterium–tritium (DT) fuel to ignition but only ∼107 J/g to compress DT to ∼1000 times solid density, a typical density for inertial fusion. To achieve such low compression energy, the fuel must be nearly Fermi-degenerate. In other words, the specific energy in the fuel must not substantially exceed the Fermi specific energy (105 J/g for solid-density DT). Because the compression energy is low compared to the ignition energy, it is advantageous to compress most of the fuel in a nearly degenerate state and to ignite as little fuel as possible. The thermonuclear burn, under appropriate conditions, can then propagate into the remainder of the fuel. In volume ignition, the entire mass of fuel is heated to ignition so one must supply 109 J/g even if the fuel is initially compressed using 107 J/g. Targets that rely on volume ignition have the lowest energy gain. In hot-spot ignition, a small portion of the fuel in the target is placed on a sufficiently high adiabat that the compression process heats it to ignition. Unfortunately, the compression process must be done sufficiently rapidly that the rate of heating the fuel exceeds conductive and radiative loss rates. The rate of heating depends on the implosion velocity. The velocity needed for ignition exceeds the velocity needed for compression, but not by a large factor. Therefore targets using hot-spot ignition have predicted energy gain that exceeds the predicted energy gain of targets that use volume ignition. If it is possible to separate the compression process and the ignition process, it should be possible to achieve even higher energy gain. Shock ignition and fast ignition are proposed methods of separating the two processes. It is assumed that the reader is familiar with the physics of these various implosion and ignition modes. There are excellent references for those who are not [1], [2]. For the purposes of this paper it is only necessary to recognize that in fast ignition, the igniting fuel is directly heated by a high-power pulse from the driver.

Although target gain is expected to increase as one moves from volume ignition to fast ignition, the accelerator constraints become more stringent. Targets designed for hot-spot ignition usually require a focal spot radius of a few millimeters and a pulse duration of several nanoseconds. In contrast, fast ignition targets typically require a focal spot radius of the order of 100 μm and a pulse duration of the order of 100 ps. Past studies [3], [4] have shown that it can be difficult to meet even the more relaxed requirements so meeting the more stringent requirements is a major issue for fast ignition.

As one moves horizontally from fully indirect drive to fully direct drive, the efficiency of coupling beam energy to the fuel increases. This increase in efficiency leads to lower driver energy requirements and higher target gain. On the other hand, requirements on beam smoothness, beam shape, and beam alignment are more stringent at the direct drive end of the spectrum

Now consider the third axis, target size. Larger targets lead to more relaxed phase-space constraints, lower technical risk, and lower target fabrication costs per joule of output energy, but they also lead to higher driver capital cost. Ultimately the goal is to find the overall target-accelerator optimum in the three-dimensional space.

The different classes of targets have different implications for heavy ion fusion development. For indirect drive with hot-spot ignition, the current laser experiments at the National Ignition Facility (NIF) are highly relevant. The ability to test indirect drive for a variety of drivers was an important justification for building NIF [5]. NIF experiments do not address the conversion of ion energy to radiation, but this physics has been tested to about 60 eV using light ions [6]. If NIF is successful with indirect drive it will boost the credibility of heavy ion indirect drive. Regardless of the results from NIF, it is important to consider other types of targets. Although beam quality and alignment are more demanding for direct drive than for indirect drive, the power, energy, focal spot radius, and ion kinetic energy requirements are similar – except at the extreme direct end of the direct-indirect spectrum. It is likely that the same accelerator could be used to explore much of the entire range. In contrast, accelerators for fast ignition appear to be quite different. In the opinion of the author, this is an important programmatic issue for ion fast ignition. It is difficult to get strong experimental confirmation that it will work without building a specialized accelerator to test it.

Section snippets

Target physics issues

There has been significant work on the physics issues associated with ion indirect drive and hot-spot ignition [7], [8], the lower left region of Fig. 1. As noted, NIF is also relevant to this region. Consequently, this section will primarily deal with fast ignition and direct drive, the upper right region of Fig. 1.

Uncertainties in accelerator and beam physics strongly influence the performance of such targets. The characteristic size and mass of the fuel that must be directly heated is set by

Accelerator and beam physics issues for fast ignition

Based on considerations of beam brightness and longitudinal dynamics, it is likely that the fractional momentum spread at the end of a heavy ion accelerator will be ≥10−4 [3], [15]. At this point the pulse duration is typically ∼100 ns. A target that uses hot-spot ignition typically requires a pulse duration of several nanoseconds. If longitudinal emittance (the product of momentum spread and beam length) is conserved during compression, the fractional momentum spread at the target would be ∼10−3

Summary

Historically a large number of heavy ion target designs have been studied. Much of the physics of indirect drive for all drivers is currently being tested at NIF. In principle, ion fast ignition can achieve higher gain than the more conventional ion targets. Nevertheless, there are a number of issues and problems that must be studied and overcome before ion fast ignition can be considered a viable option.

Acknowledgments

The author thanks Robyn Getz for help preparing the paper and for a number of valuable suggestions.

This work was supported by the Director, Office of Science, Office of Fusion Energy Sciences, of the U.S. Department of Energy under Contract no. DE-AC02-05CH11231.

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