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Transcript
The Discovery and Interpretation of the Cerenkov effect The observance of the Cerenkov effect in 1934 and the subsequent work Pavel Cerenkov performed in order to characterize the electromagnetic radiation of the same name has proven to be of substantial use in the fields of high energy and nuclear physics in later years. The apparent “blue glow” that develops in modern detectors when charged particles move through a substance at a speed greater than the phase velocity of light in the same medium provides information as to the nature of the particles as well as their supposed origin. Because of the practical applications for his work, Cerenkov was awarded the Nobel Prize in Physics in 1958 along with fellow researchers Frank and Tamm who developed the theory relating the required speeds with the unidirectional nature of the emitted radiation. Although Pavel Cerenkov is often credited with the discovery of this particular form of asymmetric radiation, decades of research into the luminescence of known lightemitting substances had been conducted by many scientists including Pierre and Marie Curie. Due to the induced luminescence marked by excited states lasting approximately 10-10 seconds, the desired phenomena was masked throughout the dying-out process; associates of Cerenkov, most notably S.I. Vavilov, were first to detect the aforementioned type of radiation via visual photometry. To examine the physical properties of the fluids, the “quenching method” was employed so as to reduce the amount of familiar luminescence by contamination with foreign reagents or by heating, consequently altering the polarization of the emitted light as well. A diagram of one of Cerenkov‟s original quenching photometers can be found in the appendix (see Figure 1); the enlarged image produced by the ocular lens, L, from reflected light of vessel A was slowly 1 distorted by the movement of a grey wedge until light was no longer capable of forming a visual image on the retina of their eyes. It was observed, however, that all of the fluids studied radiated a “blue glow” which may still have been attributed to luminescence. Whereas all known fluorescing solutions reacted in accordance with expectations predicted by experimental data, the intensity and polarization of the desired radioactive emissions in solution remained unchanged such that “the main direction of the vector of the electric vibrations did not run perpendicularly to the exciting beam, as in the case with polarized fluorescence, but parallel to it”.1 This principle was established from further testing by means of magnetic fields to characterize the behavior and propagation of this secondary radiation. In order to study the directionality of this effect, Cerenkov designed the experimental setup illustrated in Figure 2 using a conical mirror that reflected incoming radiation against a photographic plate located above a fluid-filled vessel. Photographs of the reflected light represent cases of ordinary luminescence (producing a closed ring) in addition to radiation described by two unique patches separated by an angle of 2 (see Figure 3). Experimentation with four known fluids of varying degrees of n, refractive indices, gave rise to the graphs in Figure 4 whose curves correspond to the emissions of Compton electrons that were excited by ThC and Ra gamma ray sources. These results, specifically the angular distributions of light intensities, were consistent with the proposed Tamm-Frank model for Cerenkov radiation outlined below. Based solely on electromagnetic theory as opposed to a quantum mechanical explanation provided by V.L. Ginsburg some years later, the Tamm-Frank formula 1 Cerenkov, P.A. Radiation of particles moving at a velocity exceeding that of light, and some of the possibilities for their use in experimental physics. Nobel Lecture, December 11, 1958 pp. 429 [online] 2 relates the number of photons emitted by a charged particle per unit path length and per interval unit of photon energy2: such that the angle, , according to the “mechanism of radiation” depicted in Figure 5 is defined by: cos = 1/n (2) where n is the refractive index of a particular fluid and is the standard ratio between the velocity of a particle and the speed of light as it pertains to relativistic kinetic energies. A threshold condition exists at = 1/n and = 0 in which no radiation occurs. The angle found by applying Equation 2 to known energetic particles corresponds to the observed values for theta recorded in Figure 4. A corollary to Equation 2 dictates that Cerenkov radiation is only emitted when the velocity of a charged particle in a medium with n > 1 exceeds the phase velocity of light (vp): vp = c/n (3) When the refractive index is independent of frequency as in a vacuum and for that reason a constant (dn/dk = 0), the group velocity (vg) is equal to the phase velocity whereby both values are related to one another by the formula: vg*vp = c2 (4) Accordingly, the dispersive properties within a medium maintains vg < vp. The electromagnetic field of a moving particle delocalizes nearby electrons causing them to release photons in order to achieve equilibrium following the event. Given that the 2 Govorkov, B.B. “Cherenkov detectors in Cherenkov‟s laboratory.” Lebedev Physical Institute pp. 15 [online] 3 triggered photon cascade travels slower than the field akin to a „sonic boom‟, these polarized photons will undergo constructive interference thereby contributing to the observed radiation.3 Furthermore, Frank exemplified that the direction of the radiation as determined by theta coincides with the wave model predicted by the Huygens principle such that partial waves of spherical radius equal to ct/n will “quench each other everywhere except for their common envelope”.4 The resulting wave therefore creates a cone of radiation that propagates in the same direction as the particle‟s motion with distinctive polarization characteristics initially discovered by Cerenkov post his efforts to quench luminescence and are defined by a magnetic field vector, H, tangent to the cone‟s surface as well as an electric field vector orthogonal to the light‟s direction (see Figure 6). While O. Heaviside was first to suggest „conical radiation‟ forming at the angle determined by Equation 2 nearly half a century earlier, much of his work was neglected. Orienting the graphs of Figure 4 with respect to three dimensions elucidates the structure of the cone which when projected onto a plane is a circle formed by rings of different intensities. The area of the outermost ring is composed of spectrally blue-shifted light from radiation by Compton electrons at their maximal threshold energy. Conversely, the innermost sections surrounding the center of the Cerenkov cone‟s base appear red when considering normal dispersion within the visible spectrum. To mathematically address this issue, it is necessary to consider Equation 1 in terms of the rate at which light energy, W, is produced per unit path length (note the equation cited by Cerenkov in his Nobel lecture paper is inaccurate with respect to the degree of n): 3 “Cherenkov effect” Wikipedia [online] Govorkov, B.B. “Cherenkov detectors in Cherenkov‟s laboratory.” Lebedev Physical Institute pp. 18 [online] 4 4 Applying the relationship: w = kc/n (6) since the spectrum is continuous: dW/dl = e2/c2(w2/2 – 1) (7) the final term, allowing for n to be constant, reduces to 1; differentiating with respect to the angular frequency, w: dW/dw = (e2lw)/c2 (8) which is proportional to w itself and by comparison can be expressed in wavelengths respectively as: From equation 9, it is apparent that although radiation with frequencies throughout most of the electromagnetic spectrum are theoretically assessable, shorter wavelengths begin to decrease exponentially prior to 1 and are subsequently not permitted according to relativistic kinetic energies when n is less than unity.5 Because the short wavelength cut-off for Cerenkov radiation excludes x-rays and it is probable that low frequency radiation is absorbed within solution due to atomic collisions, the “blue glow” associated with Cerenkov detectors is therefore justified. Cerenkov had calculated the threshold energies for electrons and other particles radiating for different values of n. Provided with a table of known nuclei and related energies, one can differentiate between a number of particles since the intensity of the observed radiation is “proportional to the square of the charge carried by the radiating 5 Jelley, J.V. “Cerenkov radiation and its applications.” British Journal of Applied Physics 6, 227-232 (1955) pp. 228 5 particle”. 6 The practical uses of Cerenkov radiation arise due to its unique selection for relativistic particles consequently allowing undesirable background radiation below the energy threshold to remain undetected. The added development of photomultiplier tubes (PMTs) which are capable of converting light signals into measurable electrical pulses augment the resolving power afforded with Cerenkov radiation by specifying exact particle energies and trajectories. In contrast to Cerenkov‟s original design which was a forerunner of the simple RICH detector, a modified focusing Cerenkov counter is illustrated in Figure 7 such that the velocity threshold for incoming particles is determined by the emission angle as opposed to the refractive index linked with nonfocusing counters. Of particular significance, the option of sequencing two counters sensitive for two energy thresholds has allowed scientists to identify the antiproton and other particles found within specified energy regions. 7 Despite the energy threshold required to produce directed radiation which stipulates particle selection in conjunction with the detectors later proposed by Jelley, the editors of Nature found fault with Cerenkov‟s research and declined to publish his original paper (Hubbell 1).8 Current applications for Cerenkov counters have included the detection of solar neutrinos and the investigation into cosmic ray phenomena. Large-scale detectors including the Super-Kamiokande and the Sudbury Neutrino Observatory (SNO) utilize a series of PMTs positioned around pools of „heavy water‟ to establish the origin and intensity of high energy particles via Cerenkov radiation; these particles, apart from 6 Snell, A.H. Nuclear instruments and their uses. Vol. 1. John Wiley & Sons, Inc., New York 1962 pp. 166 7 Cerenkov, P.A. Radiation of particles moving at a velocity exceeding that of light, and some of the possibilities for their use in experimental physics. Nobel Lecture, December 11, 1958 pp. 439 [online] 8 Hubbell, John H. “Faster than a speeding photon.” National Institute of Standards and Technology, August 26, 1991 pp. 1 [online] 6 secondary shower products, are chiefly comprised of electrons and positrons created when cosmic rays interact with the earth‟s atmosphere and undergo pair production. Whereas common scintillation counters are plagued by proton recoils and do not limit the amount of luminescence generated by background radiation, the extensive deployment of Cerenkov detectors is marked by their ability to characterize charged particles with respect to energy as well as path determination. 7 8 References Cerenkov, P.A. “Visible Radiation Produced by Electrons Moving in a Medium with Velocities Exceeding that of Light.” Phys. Review 52, 378-379 (1937) pp. 378-379. [online] 28 February 2005 <http://prola.aps.org/pdf/PR/v52/i4/p378_1> Cerenkov, P.A. Radiation of particles moving at a velocity exceeding that of light, and some of the possibilities for their use in experimental physics. Nobel Lecture, December 11, 1958 pp. 426-440. [online] 18 February 2005 <http://nobelprize.org/physics/laureates/1958/cerenkov-lecture.pdf> “Cherenkov effect” Wikipedia [online] 28 February 2005 <http://en.wikipedia.org/wiki/Cerenkov_effect> Govorkov, B.B. “Cherenkov detectors in Cherenkov‟s laboratory.” Lebedev Physical Institute pp. 1-36. [online] 28 February 2005 <http://www.ifisica.uaslp.mx/rich2004/talks/0003/Cherenkov_Present.ppt> Hubbell, John H. “Faster than a speeding photon.” National Institute of Standards and Technology, August 26, 1991 pp. 10. [online] 3 March 2005 <http://www.garfield.library.upenn.edu/classics1991/A1991GA09200001.pdf> Jelley, J.V. “Cerenkov radiation and its applications.” British Journal of Applied Physics 6, (1955) pp. 227-232. Snell, A.H. Nuclear instruments and their uses. Vol. 1. John Wiley & Sons, Inc., New York 1962 pp. 166-184. 9