Classical interferometry works by detecting correlations in the phases of two waves. In Nature in 1956, R. Hanbury-Brown and R. Q. Twiss demonstrated another technique that probes quantum-mechanical correlations in the electromagnetic field. Splitting an incoherent light beam, they found that photon detections in the two daughter beams were correlated: the photons were bunching together. This corresponds to a correlation in the intensity of light in the two beams, which Hanbury-Brown and Twiss suggested could be used to infer the angular size of distant stars. Physicists now rely on the effect to probe the quantum character of complex light sources. [Obituary of Robert Hanbury Brown: Nature 416, 34 (2002)]
The resolution and accuracy of a modern optical Michelson stellar interferometer are limited principally by atmospheric turbulence. To reach 9th magnitude, the maximum practicable baseline is probably about 100 meters because of large scale long period atmospheric fluctuations in optical path. Longer baselines would require narrower optical bandwidths with an associated loss in signal-to-noise ratio and, therefore, of limiting magnitude. Perhaps more important from the astronomical point of view is the loss in accuracy caused by the atmosphere. If the losses are not too large, it is feasible to estimate them by auxiliary observations, either through the same apertures or by means of seeing monitors placed near the primary apertures. Most of the instrumentation needed for a Michelson stellar interferometer has already been developed, either for the existing prototype interferometers or for other applications, so there is no reason why an interferometer with a baseline of 100 meters and a limiting magnitude of +9 cannot be built.
An interferometric technique based on a white light fringe setting was used to set mirrors defining a base plane in a Michelson stellar interferometer to coplanarity. The method is in principle capable of extension to very large separations, and the precision of visual setting is of the order of the wavelength of light.
A new 1.87 m fixed-baseline interferometer designed for binary star observation is now in operation at the Italian outstation of the Royal Observatory Edinburgh. It has a theoretical resolving power of 0.015 arcsee and a limiting B magnitude of 6.5. Atmospheric seeing is dynamically corrected, allowing a quantitative measurement of fringe visibility.
Diffraction caused by finite apertures in long baseline interferometers leads to a significant loss of signal, decreased fringe visibility, and a phase shift in the interference pattern. Formulas are developed for the general case of an interferometer with unequal path lengths for monochromatic plane wave illumination. Numerical results are given for a range of path lengths. The consequences of diffraction on the performance of long path instruments, particularly with reference to a long baseline Michelson stellar interferometer, are discussed.
The drop in visibility due to path difference errors in a Michelson stellar interferometer is normally controlled by a monochromator in the system. It is shown that the effect of this monochromator on the visibility is governed by a product of two factors, one geometrical and the other a function of the resolving power of the monochromator. The second factor causes the visibility to vanish identically for path differences exceeding a certain value. A comparison of prisms and gratings shows that in general a prism train is preferable as a dispersing device.
Criteria as to when an intensity interferometer is competitive with a Michelson interferometer are established with the help of a simple example. There do not appear to be any cases in the field of frequency measurement where this is true. In radio astronomy it is argued that intensity interferometry might still have a role in angular measurements of the very smallest sources but it is clear that the main application still lies in visual astronomy in measurements in hot single stars and close spectroscopic binaries. A discussion is given as to how far the method could be pushed both from the technical as well as from the observational aspect. The triple correlation interferometer of Gamo is considered but because of its extremely low sensitivity it seems to have no application at least in visual astronomy and in this field the use of lasers is also rejected partly because of the various serious effects of atmospheric 'seeing', and partly because of the excessively tight tolerances on the performance of the very large mirrors needed to obtain adequate sensitivity. The possibility of laboratory applications also seem remote, in particular the idea that intensity interferometry could be used at x-ray wavelengths to measure the phase of scattering amplitudes is shown to be ruled out by inadequate sensitivity which could only be overcome by the development of coherent x-ray sources.
Spectroscopy by two-beam interferometry is compared with conventional techniques and it is shown that considerable advantages may be expected in some measurements from the use of interferometers. The important advance in the last decade which allows this to be realized is the use of digital computers. Their use has also allowed the development of refractive index spectroscopy over wide spectral ranges using Michelson's interferometer. The duality of spectral and angular measurement is stressed and the potential of the spectroscopic analogue of the stellar intensity interferometer, which so far has not been developed, is analysed here.
(1963). On the difference between the amplification of longitudinal plasma waves and the negative absorption of cerenkov radiation in an electron stream. The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics: Vol. 8, No. 91, pp. 1249-1251.
view Abstract Citations (5) References (3) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On Negative Absorption in an Electron-Ion Plasma when Radiation Takes Place by Free-Free Transitions. Twiss, R. Q. Abstract A rebuttal is given of Browne's criticisms of Twiss's proof that negative absorption can never take place in an electron-ion plasma when radiation is produced by free-free transitions. It is shown that Browne's own theory gives an expression for the absorption coefficient that does not correspond to thermal equilibrium when the electron velocity distribution is Maxwellian. It is concluded that Browne's theory is wrong and his conclusions invalid. Publication: The Astrophysical Journal Pub Date: September 1962 DOI: 10.1086/147396 Bibcode: 1962ApJ...136..438T full text sources ADS |
A criticism is given of a recent paper by Piddington with the same title. It is shown that his belief that the growing waves in a two-stream electron wave tube are really evanescent is untenable and that his own theory is effectively equivalent to the conventional one in which these growing waves are identified as being true amplified waves. Piddington's conclusion that an initial disturbance in a two-stream medium will grow exponentially with time without oscillation is shown to be a consequence of highly idealized assumptions as to the nature of the medium and as to the initial and boundary conditions. In any practical case it is argued that double stream flow will build up oscillations at frequencies, in general around the plasma frequency, rather than produce charge separated blobs as in Piddington's theory. If temperature effects are allowed for it is shown that double stream flow does not occur in the corona in the case discussed by Piddington and reasons are also given for rejecting a theory of growing waves in shock fronts advanced by Sen. Piddington's reasons for rejecting the existence at transverse space charge waves in a drifting ionized medium and for denying that growing evanescent waves can, be excited by reflection are shown to be invalid. This removes Piddington's objection to an earlier theory of excess solar radio wave put forward by the writer, but it is agreed that this theory must now be rejected on other grounds.
A theory is given for the radiation from a fast electron rotating, under the action of an external magnetic field, in an ionized plasma. It is shown that, although the radiation is emitted predominantly in the extraordinary mode, the ordinary mode is also weakly excited, even in the limiting case in which the density of the background plasma is vanishingly small. At the harmonics of the gyro frequency of the fast electron the power radiated in the ordinary mode is a few per cent. of that radiated in the extraordinary mode. This ratio is independent of v0,' the velocity of the fast electron, as long as V0 is sufficiently small compared with c, the velocity of light. However, at the fundamental gyro frequency the power radiated in the ordinary mode is lower by a factor than that radiated in the extraordinary mode and indeed is significantly smaller than that radiated, in either mode, at the third harmonic.
Stimulated transitions are relatively enormously more probable at radio than at optical frequencies and it is this which makes it possible for negative absorption to arise at radio wavelengths when the medium will behave like an amplifier to the incident radiation. A necessary condition for the existence of this phenomenon is that the kinetic energy distribution F(?) of the radiating electrons be markedly non-thermal with an appreciable excess of high energy electrons such that F/? is positive over a finite range of the kinetic energy ?. However, this condition is not sufficient, since it is shown that an electron gas in which freefree transitions provide the dominant radiation process can never exhibit negative absorption whatever the form of F(?), and it is further necessary that the stimulated transition probability should have a maximum at some finite value of the kinetic energy, the most favourable case occurring when this maximum is a sharp one at the value of ? at which F/? has a positive maximum. These conditions can both be met in principle for the cases in which the dominant radiation process is due (a) to Cerenkov effect, (b) to gyro radiation by non-relativistic electrons, (c) to synchrotron-type radiation by highly relativistic electrons, and it is shown that negative absorption can arise in all these cases; the relevance of these results to radio astronomy is discussed briefly.
SUMMARY Numerical calculations are given for the space charge distribution in a cylindrical magnetron diode, which allow for the thermal emission velocities but neglect electron–electron interaction. In all cases the distribution is of double stream type even when the ratio of the radius of the space charge cloud to the cathode radius is less than two. However, the results obtained are not in agreement with experimental data, described in the companion paper, and a brief outline is given of the lines on which a correct theory might be set up.
The theory that the galactic radio noise emitted by the discrete sources is due to the interaction of a local magnetic field and cosmic ray electrons is tested quantitatively for the source in Cassiopeia. It is shown that the average magnetic field must be of the order of 0·01 gauss, which is approaching the upper limit imposed by energy considerations. At frequencies below 15 Mc/sec resonant reabsorption of the r.f. energy becomes important and if the theory is valid the r.f. power received at the earth should vary at least as rapidly as v 5/2 below a critical frequency in the range 10–20 Mc/sec.
This chapter presents the theoretical analyses of the preoscillation state in the cylindrical and linear magnetrons that fall into two distinct classes. In one treatment, the electron cloud is replaced by a charged fluid and the electron-electron scattering is ignored. The orbit followed by a given electron is then completely determined by its emission velocity and the external fields, and there is a completely ordered flow. The alternative treatment, based on statistical mechanics, assumes complete local disorder. Conditions in a physical magnetron will lie somewhere between these two extremes, but the exact theory is exceedingly complicated and there is little prospect that it can be carried through in quantitative form.
A critical discussion is given of the conventional procedure for determining whether a particular electron stream is unstable It is shown that in some cases where this analysis suggests instability the stream is stable, while in others, where instability does occur, neither the frequency nor the rate of build up of oscillations are as predicted. The physical causes of instability in an electron stream are also considered.
The theory of the electron synchrotron has been amply covered elsewhere, but the proton synchrotron exhibits a number of distinct but important differences particularly at low energies. In the present paper the theory for this latter accelerator is developed with particular reference to the problems of injection and stability in the initial acceleration period. This theory is used to set up criteria relating the dimensions of a proton synchrotron to the conditions for stability and to the beam intensities obtainable.
