Accurate x-ray scattering techniques to measure the physical properties of dense plasmas have been developed for applications in high energy density physics. This class of experiments produces short-lived hot dense states of matter with electron densities in the range of solid density and higher where powerful penetrating x-ray sources have become available for probing. Experiments have employed laser-based x-ray sources that provide sufficient photon numbers in narrow bandwidth spectral lines, allowing spectrally resolved x-ray scattering measurements from these plasmas. The backscattering spectrum accesses the noncollective Compton scattering regime which provides accurate diagnostic information on the temperature, density, and ionization state. The forward scattering spectrum has been shown to measure the collective plasmon oscillations. Besides extracting the standard plasma parameters, density and temperature, forward scattering yields new observables such as a direct measure of collisions and quantum effects. Dense matter theory relates scattering spectra with the dielectric function and structure factors that determine the physical properties of matter. Applications to radiation-heated and shock-compressed matter have demonstrated accurate measurements of compression and heating with up to picosecond temporal resolution. The ongoing development of suitable x-ray sources and facilities will enable experiments in a wide range of research areas including inertial confinement fusion,more » radiation hydrodynamics, material science, or laboratory astrophysics.« less

X-ray Thomson scattering in high energy density plasmas

The application of Thomson (or incoherent) Scatter observations to the study of the earth's ionosphere is described. Those aspects of theory of Thomson Scatter that have been put to practical use in ionospheric investigations are reviewed briefly and the type of radar equipment constructed for these investigations is discussed. Methods of measuring electron density, electron and ion temperatures, and ionic composition are then reviewed. Other applications of the technique--to the study of the neutral density and temperature of the upper atmosphere, drift motions, the flux density of fast photoelectrons, and the orientation of the earth's magnetic field--are also described.

Theory and practice of ionosphere study by Thomson scatter radar

The theory of light scattering from a collection of free electrons is reviewed, and it is shown that the frequency spectrum observed at a detector is precisely that of the density fluctuations of a particular scale length in the scattering medium, the scale length being determined by the wavelength of the incident light and the geometry of the experimental arrangement. The electron density fluctuation in a plasma is calculated, and it is shown that the plasma Debye shielding distance λD is a critical length in the theory, the electrons behaving independently on a scale shorter than λD and collectively on a scale longer than λD. The collective behaviour is characterized by the presence of waves that can give rise to well-defined resonances in the scattered-light spectrum. The effects of differing ion and electron temperatures, current flowing in the plasma, magnetic field, and Coulomb collisions are considered briefly. Technical considerations in planning experiments to test the theory and to apply it to the diagnosis of real laboratory plasmas are discussed, with attention being given to signal-to-noise ratio, stray light, and the dispersing instrument to be used at the detector. Some representative experiments that have been carried out are reviewed.

https://iopscience.iop.org/article/10.1088/0034-4885/32/1/305/pdf

Laser light scattering in laboratory plasmas

With the incoherent scatter facility at Chatanika, Alaska, we have measured electron temperatures of up to 1200/sup 0/K near 110-km altitude in the polar E region in the presence of strong electric fields. No classical heat process can account for these high temperatures, which are clearly correlated with the dc electric field strength. We show that the enhancement is most probably caused by the unstable plasma waves known to exist in the disturbed polar E region.

Anomalous heating of the polar E region by unstable plasma waves 1. Observations

The theory of incoherent scattering in a plasma is extended to include the effect of ions and electrons colliding with neutral molecules, an effect that could be important in the ionosphere below perhaps 150 km for experiments at frequencies of the order of 50 Mc/s or less. We find, first of all, that the total scattered power is completely independent of collisions; the collisions only affect the shape of the spectrum. If, as is usually the case, the Debye length [6.9 (T/N)1/2 cm] is small compared to λ/4π. (λ is the radio wavelength), the spectrum begins to become narrower and peaked at the center when the mean free path of the ions becomes comparable to λ/4π. Any possible ion gyroresonant effects on the spectrum due to the presence of a magnetic field will be prevented if the collision frequency of the ions is greater than or equal to their gyrofrequency. If the Debye length should happen to be greater than λ/4π, the above comments would apply to the mean free path, collision frequency, and gyrofrequency of the electrons; however, such electron effects are not likely to be important in the ionosphere. It does seem that perhaps we might be able to measure ion collision rates by means of incoherent scattering. The principal difficulty would be in obtaining, from low altitudes, incoherent scattering signals uncontaminated by other types of scattering.

A theory of incoherent scattering of radio waves by a plasma: 3. Scattering in a partly ionized gas

A theory is developed which describes the scattering of radio waves by the random thermal fluctuations of electron density in a collision-free plasma. The frequency spectrum, as well as the amplitude, of the scattered radiation is calculated. Particular attention is paid to the part of the spectrum which corresponds to small Doppler shifts, this being the region of greatest significance in connexion with the phenomenon of incoherent scattering from the ionosphere. The calculations are based on a generalized version of Nyquist's noise theorem, and they lead to the following conclusions: (1) The mean scattering cross-section for the ionosphere is equal to that which would exist if each of the electrons scattered independently with a cross-section of one-half the classical Thomson cross-section. (2) The mean Doppler broadening of the scattered signal corresponds roughly to the speed of the ions rather than to that of the electrons. (3) The spectral shape of this signal is not Gaussian. There is a mild maximum in the spectrum away from the central frequency, as can be seen in figure 1. (4) Plasma resonance effects contribute only negligibly to the scattering for frequencies currently of interest.

A theory of incoherent scattering of radio waves by a plasma

A general expression for the frequency spectrum of radio waves scattered by random thermal fluctuations of electron density in a plasma in a magnetic field is derived. The derivation is based on the generalized Nyquist noise theorem. The result is simplified by an approximation assuming the velocity of light to be infinite. It is shown that this approximation is adequate for ionospheric applications of the theory. Next it is proved, without appealing to any approximation, that the magnetic field can never alter the total scattered signal power; it can only redistribute this power over the spectrum. Finally, the detailed shape of the frequency spectrum of the scattered signal is examined. Analytic expressions are given for certain limiting cases, but for cases of most interest, numerical methods must be used. Results of numerical calculations are shown. From these results, it can be seen that the magnetic field has a significant effect on the shape of the spectrum only if the incident radio beam is very nearly orthogonal to the magnetic lines of force. For example, for an operating frequency of 40 Mc/s, no significant magnetic effect is observed even when the beam is within 5 deg of orthogonality. As this anglemore » is decreased further, however, the spectrum rapidly begins to develop spikes at Doppler shifts which are approximate multiples of the ion gyro-frequency. These spikes are quite pronounced when the beam is 2 deg from orthogonality. At higher operating frequencies, the beam must be proportionally closer to orthogonality to achieve the same effect. (auth)« less

A theory of incoherent scattering of radio waves by a plasma. ii. scattering in a magnetic field

This paper describes a theory of the resonant effects observed by sounding equipment on the ionospheric satellite 'Alouette'. The model consists of an oscillating dipole immersed in a uniform hot plasma with uniform magnetic field. A formal expression for the electric field throughout space is readily constructed. In simple cases (zero temperature and either no magnetic field or infinite light velocity) this reduces to an integral which can be evaluated analytically and the resonance shown explicitly. In general we try to locate the frequencies at which resonance will occur without evaluating the field. This can be done by the 'pinching-poles' technique used in quantum field theory. The results show that resonances would occur at the following frequencies: the plasma frequency, $\omega\_p$; the gyrofrequency of the electrons, $\Omega\_e$ and its harmonics n$\Omega\_e$, the 'hybrid' frequency, ($\omega^2\_p$ + $\Omega^2\_e$)$^\frac{1}{2}$, and the 'zero range' frequencies, which satisfy $\omega^2 \pm \Omega\omega - \omega^2\_p = 0.$ Some idea of the relative importance of these resonances can also be gained for the theory. The fundamental of the gyrofrequency series, and the zero-range frequencies, would give only weak resonances. The series $\omega$ = n$\Omega_e$ has a complicated structure, and is really the superposition of four series, some of which are slightly shifted from the exact harmonics.

J. P. Dougherty

Papers

A theory of incoherent scattering of radio waves by a plasma

A theory of incoherent scattering of radio waves by a plasma. ii. scattering in a magnetic field

Theory of resonances observed in ionograms taken by sounders above the ionosphere