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Emission of radiation at short wavelengths demands hot plasmas, which are readily produced by the pinch effect. This term describes the self-constriction accompanied by heating of discharges by the magnetic field B of the current I in a discharge plasma. Pinching starts when the magnetic field pressure B2∕2μ0 exceeds the plasma particle pressure p, and it stops when the two are equal; this condition describes a magnetically confined plasma column. There are two complementary geometries: the linear, or Z, pinch and the Θ pinch (Fig. 6.1). Both are axially symmetric. In the Z pinch the current flows along the axis (Z direction) and the plasma is confined by the azimuthal magnetic field of the current. In the second arrangement an azimuthal current (in the Θ direction) is induced in the plasma column by a rapidly varying current in a single-turn coil around the discharge vessel, and the confining magnetic field is parallel to the axis. Both discharges are operated in a pulsed mode, since the high currents required can conveniently be supplied only by discharging properly designed capacitor banks. Operation in pulsed mode is useful also for other reasons: the lifetime of hot plasma columns is limited by plasma losses at the ends of the column on the one hand, and on the other hand these plasmas are prone to hydromagnetic instabilities, which are extremely serious in the case of the Z pinch. However, the transformation of electrical energy into plasma is rather inefficient in Θ-pinch devices of short length; thus nearly all discharge-based EUV sources employ the linear geometry. A typical Z-pinch discharge proceeds as follows: high voltage is applied to the electrodes of the discharge tube, and after breakdown the current starts to flow in a thin cylindrical low-temperature plasma shell adjacent to the insulating wall. This current produces a corresponding magnetic field outside the shell, which accelerates the plasma like a piston or a slug toward the axis till it stagnates on the axis. For rough estimates, modeling of the compression employing a simple “snowplow” model suffices, although a detailed description of the plasma state requires solving MHD equations combined with kinetic codes for ionization and population of the atomic species, taking into account also radiative transport. A cylindrical shock wave running ahead of the piston is characteristic of fast discharges. Several calculations are presented in this book; see, for example, Chapter 11. In this chapter we focus on the development of a magnetically confined plasma cylinder consisting of strongly radiating ions after it has been formed on the axis. In this state, energy is transferred to the plasma mainly by Joule heating.
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