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Pulsed high beta plasmas
Annals of Nuclear Enerffy, Vol. 4, pp. 471 to 474. Pergamon Press 1977. Printed in Great Britain
BOOK REVIEWS Pulsed High Beta Plasmas This book is the proceedings of the third topical conference on pulsed high beta plasma held at Culham Laboratory in September 1975. For engineers and scientists not familiar with the nomenclature of the title, it refers to magnetic containment devices in which the ratio of plasfna pressure to magnetic pressure is in the range 10-100~o. These devices are usually pulsed for one of two reasons. Either they refer to straight configurations which rely on compression and shock heating and which have end losses and last only for a few ion transit times, or else they are toroidal but last only for a time characterized by the time for the diffusive evolution of the magnetic fields in the plasma to yield an unstable or a low fl configuration. The first category includes theta pinches and the plasma focus, whilst the second includes the reversed-field-pinch (RFP) the screw pinch, and the high beta Stellarator and Tokamak. The conference was evenly divided between these categories. Of the 97 papers 21 were on the 0 pinch, 8 on the plasma focus, 22 on RFP, and 8 each on the screw pinch, the belt pinch and the high beta Stellarator and Tokamak. From the geographical point of view 45 of the papers came from the USA, 19 from the UK but only 2 from Russia. So one could rightly question the balance of coverage of the meeting. Many of the papers reported incomplete work which would not normally get published except in a proceedings of this sort. Indeed many papers would not survive refeering for a reputable journal. The attraction of high/3 from the controlled fusion point of view is that the nuclear reaction rate proceeds as n 2 at a temperature which must be about 12 keV for D-T reactions. Therefore for a given magnetic field and temperature there is a quadratic dependence of the reaction rate on fl, and the required confinement time (to satisfy the Lawson criterion) varies inversely with ft. However the gain achievable from an increase in local fl can be offset by the reduction in plasma volume compared to the volume occupied by the magnetic field in a compressional system, too high a radiative wall loading, and an expensive pulsed magnetic energy storage system, apart from a greater difficulty in achieving a stable equilibrium. Feedback, finite Larmor radius, and even conducting wall stabilization, whilst practical in a small laboratory system, may not be applicable to a reactor size device. The reader should read these papers therefore with some caution, and realize that most of these devices are still in the (rather interesting) physics stage where the basic plasma behaviour is being investigated. To highlight some of the work contained in this volume, first there are the disappointing results on the high fl stellarators at Garching and Los Alamos where the high values of density ( 2 x 10~6cm -a) ion temperature (0.8 keV) and fl (~0.8) were offset by the short stability time of 10 #s, representing one sound transit time. Because the density and temperature were achieved by compression, wall stabilization of the m = 1 mode was ineffective.
No diffuse three dimensional equilibria have been found theoretically yet, but the stability of the nearest equivalent straight cylinder is shown to require finite ion Larmor radius effects to stabilize m > 2. The theoretical and experimental work on theta pinches concentrated mainly on the structure of the collisionless shock in the presence of electrostatic turbulence, with present interest centred on the lower hybrid drift mode. This might be relevant to shock heating of a toroidal high fl stellarator. The reversed field pinch is of particular interest to Culham Laboratory, mainly because of the self generated field reversal found experimentally in ZETA over a decade ago. By having a monotonic variation of axial magnetic field with reversal of sign near the wall it is possible to maintain adequate shear and satisfy Suydam's stabihty criterion everywhere (except possibly near the axis). Accounts of more recent experiments together with an energy principle argument for a slightly resistive plasma were presented, but at this conference the only theory showing how self reversal might occur relied on a very particular model of MHD turbulence. Screw pinches and belt pinches have essentially become high fl versions of Tokamaks, In both systems the role of the low density force free plasma in the outer regions was discussed and clearly requires further investigations as it is a source of turbulently driven anomalous resistivity and of X-rays. In belt pinches the high fl (e.g. 0.5 at Lausanne) drops as the elongated cross section contracts through evolution of the equilibrium. Stability of the high curvature regions is also a problem if the cross-section is too elongated. The intrepid band of plasma focus enthusiasts, claimed (from Limeil) a neutron yield scaling with current to the power of 3.3 over 105 to 2 x 106A. Laser scattering measurements showed a high level of fluctuations due to waves propagating parallel to the current, the high resistance associated with these being a possible explanation of the voltage spike common to these devices. Related to the focus was a paper postulating the beneficial effects of a dense neutral gas surrounding a z pinch in a reactor concept. The Russians showed their interest in liner compression of plasmas and envisage obtaining 2 MG magnetic fields and a density of 1019. This is certainly an area of engineering ingenuity in which the US Naval Research Laboratory also take part. In summary, this book records fairly accurately the present scenario of some (off-beaff) areas of controlled fusion outside the main research streams of Tokamaks, mirrors and inertial containment. Engineers will find the concepts less well developed than, say, Tokamaks, but we are approaching the time when the engineering consequences of some of these fusion schemes need to be soberly evaluated.
Imperial College University of London.
471
I~OFESSOR M. G. I-b.~qES
BOOK REVIEWS Pulsed High Beta Plasmas This book is the proceedings of the third topical conference on pulsed high beta plasma held at Culham Laboratory in September 1975. For engineers and scientists not familiar with the nomenclature of the title, it refers to magnetic containment devices in which the ratio of plasfna pressure to magnetic pressure is in the range 10-100~o. These devices are usually pulsed for one of two reasons. Either they refer to straight configurations which rely on compression and shock heating and which have end losses and last only for a few ion transit times, or else they are toroidal but last only for a time characterized by the time for the diffusive evolution of the magnetic fields in the plasma to yield an unstable or a low fl configuration. The first category includes theta pinches and the plasma focus, whilst the second includes the reversed-field-pinch (RFP) the screw pinch, and the high beta Stellarator and Tokamak. The conference was evenly divided between these categories. Of the 97 papers 21 were on the 0 pinch, 8 on the plasma focus, 22 on RFP, and 8 each on the screw pinch, the belt pinch and the high beta Stellarator and Tokamak. From the geographical point of view 45 of the papers came from the USA, 19 from the UK but only 2 from Russia. So one could rightly question the balance of coverage of the meeting. Many of the papers reported incomplete work which would not normally get published except in a proceedings of this sort. Indeed many papers would not survive refeering for a reputable journal. The attraction of high/3 from the controlled fusion point of view is that the nuclear reaction rate proceeds as n 2 at a temperature which must be about 12 keV for D-T reactions. Therefore for a given magnetic field and temperature there is a quadratic dependence of the reaction rate on fl, and the required confinement time (to satisfy the Lawson criterion) varies inversely with ft. However the gain achievable from an increase in local fl can be offset by the reduction in plasma volume compared to the volume occupied by the magnetic field in a compressional system, too high a radiative wall loading, and an expensive pulsed magnetic energy storage system, apart from a greater difficulty in achieving a stable equilibrium. Feedback, finite Larmor radius, and even conducting wall stabilization, whilst practical in a small laboratory system, may not be applicable to a reactor size device. The reader should read these papers therefore with some caution, and realize that most of these devices are still in the (rather interesting) physics stage where the basic plasma behaviour is being investigated. To highlight some of the work contained in this volume, first there are the disappointing results on the high fl stellarators at Garching and Los Alamos where the high values of density ( 2 x 10~6cm -a) ion temperature (0.8 keV) and fl (~0.8) were offset by the short stability time of 10 #s, representing one sound transit time. Because the density and temperature were achieved by compression, wall stabilization of the m = 1 mode was ineffective.
No diffuse three dimensional equilibria have been found theoretically yet, but the stability of the nearest equivalent straight cylinder is shown to require finite ion Larmor radius effects to stabilize m > 2. The theoretical and experimental work on theta pinches concentrated mainly on the structure of the collisionless shock in the presence of electrostatic turbulence, with present interest centred on the lower hybrid drift mode. This might be relevant to shock heating of a toroidal high fl stellarator. The reversed field pinch is of particular interest to Culham Laboratory, mainly because of the self generated field reversal found experimentally in ZETA over a decade ago. By having a monotonic variation of axial magnetic field with reversal of sign near the wall it is possible to maintain adequate shear and satisfy Suydam's stabihty criterion everywhere (except possibly near the axis). Accounts of more recent experiments together with an energy principle argument for a slightly resistive plasma were presented, but at this conference the only theory showing how self reversal might occur relied on a very particular model of MHD turbulence. Screw pinches and belt pinches have essentially become high fl versions of Tokamaks, In both systems the role of the low density force free plasma in the outer regions was discussed and clearly requires further investigations as it is a source of turbulently driven anomalous resistivity and of X-rays. In belt pinches the high fl (e.g. 0.5 at Lausanne) drops as the elongated cross section contracts through evolution of the equilibrium. Stability of the high curvature regions is also a problem if the cross-section is too elongated. The intrepid band of plasma focus enthusiasts, claimed (from Limeil) a neutron yield scaling with current to the power of 3.3 over 105 to 2 x 106A. Laser scattering measurements showed a high level of fluctuations due to waves propagating parallel to the current, the high resistance associated with these being a possible explanation of the voltage spike common to these devices. Related to the focus was a paper postulating the beneficial effects of a dense neutral gas surrounding a z pinch in a reactor concept. The Russians showed their interest in liner compression of plasmas and envisage obtaining 2 MG magnetic fields and a density of 1019. This is certainly an area of engineering ingenuity in which the US Naval Research Laboratory also take part. In summary, this book records fairly accurately the present scenario of some (off-beaff) areas of controlled fusion outside the main research streams of Tokamaks, mirrors and inertial containment. Engineers will find the concepts less well developed than, say, Tokamaks, but we are approaching the time when the engineering consequences of some of these fusion schemes need to be soberly evaluated.
Imperial College University of London.
471
I~OFESSOR M. G. I-b.~qES