The observation of a shadowing effect of a relativistic electron Coulomb field for the Smith-Purcell radiation generation is presented in this paper. For this purpose the surface current from the closest surface of grating element

to the electron beam was measured for a downstream one shadowed by upstream element. The experimental results showed that shadowing effect for Smith-Purcell radiation depends on grating geometry

Naumenko, G. A.

Popov, Yu. A.

Potylitsyn, A. P.

Shevelev, M. V.

English

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DOI 10.1393/ncc/i2011-10942-6Colloquia: Channeling 2010IL NUOVO CIMENTO Vol. 34 C, N. 4 Luglio-Agosto 2011Experimental test of the shadowing effectin Smith-Purcell radiationG. A. Naumenko(∗), A. P. Potylitsyn, Yu. A. Popov and M. V. ShevelevPhysical and Technical Institute, Tomsk Polytechnic UniversityLenin Ave. 2a, 634050 Tomsk, Russia(ricevuto il 22 Dicembre 2010; pubblicato online il 25 Agosto 2011)Summary. — The observation of a shadowing effect of a relativistic electronCoulomb field for the Smith-Purcell radiation generation is presented in this pa-per. For this purpose the surface current from the closest surface of grating elementto the electron beam was measured for a downstream one shadowed by upstreamelement. The experimental results showed that shadowing effect for Smith-Purcellradiation depends on grating geometry.PACS 41.60.-m – Radiation by moving charges.PACS 41.90.+e – Other topics in electromagnetism; electron and ion optics.1. – IntroductionThe shadowing of an electron electromagnetic field in case of diffraction and transitionradiation was considered theoretically and experimentally in a number of papers [1-5]. Inthe pseudo-photon approach for ultra-relativistic electron the properties of electron fieldsare very close to the properties of real photons. Namely, the field may be considered asa transversal one. There is a region downstream to the conductive or absorbing screenwhere the Coulomb field is partly missing. In terms of paper [2] this effect is named“shadow effect”, and the term “semi-bare electron” has been introduced in [6, 7] todescribe a similar effect in the framework of quantum electrodynamics for an electronscattered at a large angle.For a transversal component of the electromagnetic field of a relativistic electron thiseffect may be simple explained in the frame of pseudo-photon approach [3]. In [4] theshadowing effect for a Smith-Purcell radiation (SPR) was predicted by Prof. X. Artru(see fig. 1), where the author had noted that the mere addition of the diffraction radiationamplitudes from the different strips neglects the shadow effect, and therefore overestimatethe SP intensity.(∗) E-mail: naumenko@tpu.ruc© Societa` Italiana di Fisica 305306 G. A. NAUMENKO, A. P. POTYLITSYN, YU. A. POPOV and M. V. SHEVELEVFig. 1. – (Figure 6 from [4].) Shadowing in a periodical target.For the experimental test of this effect we may adopt the following method. As shownin [8] the Smith-Purcell radiation may be considered as a resonant backward diffractionradiation. According to [9, 10] in this geometry the surface current viewpoint may beapplicable. Radiation from each grating element is defined by the surface current on thesurface of the element and the total radiation in the far-field zone results by interferenceof radiation from all elements of grating. Therefore the problem may be resolved bymeasurement and comparing of the surface current, induced by an electron beam on thenot shadowed and shadowed strip.For the simplest grating consisting of a set of conducting strips separated by vacuumgaps and locating in a plane the surface current Js induced by a charge q moving par-allel to the grating may be calculated using the approach developed in the paper [11].Generally speaking the surface current is proportional to the transversal component ofthe charge electric field:(1) Js(ω) ∼ E0⊥ ∼ q · exp[−hωcγ],where the last multiplier describes the decay of Fourier component of a field with fre-quency ω, h is the impact-factor (the shortest distance between charge and grating), γ isLorentz factor.The shadowing effect in these terms may be introduced as the suppression of a fieldE⊥ at distance l  γ2 2πcω = γ2λ from the upstream strip along particle trajectory. Itmeans the surface current induced on a strip surface will decrease beginning from thefirst one.2. – ExperimentThe experiment was performed on the extracted electron beam of microtron of TomskNuclear Physics Institute with parameters shown in table I. The electron beam is ex-tracted from the vacuum chamber through the beryllium foil with a thickness of 40μm.Table I. – Electron beam parameters.Electron energy 6.1MeV (γ = 12) Bunch period 380 psTrain duration τ ≈ 4μs Train repetition 6HzBunches in a train nb ≈ 1.6 · 104 Bunch length σ ≈ 2mmBeam size σB ≈ 2mm Bunch population Ne = 6 · 108EXPERIMENTAL TEST OF THE SHADOWING EFFECT IN SMITH-PURCELL RADIATION 307Fig. 2. – Active element of SPR target.We apply the well-known technique, which is used in strip-line beam position moni-tors [12]. This sensor registered a surface current component perpendicular to the slits(see fig. 2). The signal from the sensor is rectified by a high-frequency diode for rec-tification of the signal with frequency up to 100GHz. The rectified signal was directlymeasured using a charge-digital converter without amplifier.The distance L between the slits was chosen to be 4mm (the quarter of the averagewavelength of a registered SPR). According to [12] the strip-line pickup usually operatein a spectral interval between the 3 dB points of the first lobe c8L < f <3c4L (heref = ω2π ) with maximum of the sensitivity in the point fmax =c4L , i.e. for our sensor10GHz < f < 60GHz with maximum in the point fmax = 20GHz. The slit widthwas 0.4mm. The described sensor was inserted in the element typical for a SPR targetelement (active element). To be sure that we measure the concerned amount, we hadmeasured the dependence of the surface current on the impact parameter (dots in fig. 4)for single grating element in the geometry shown in fig. 3.The solid line in fig. 4 is the fit of function (1) to the experimental data. The fit isshown for γ = 12 and ω = 1.02 · 1011 (i.e. f = 16.2GHz). Here f is to be assumed as anaverage value in the investigated spectral region. This value is in good agreement withexperimental conditions. The value of J for h = 5mm is 90± 10 channels CDC.For measuring the shadowing effect we had inserted three grating elements of thesame geometry but without a sensor (passive elements) upstream to the active element(see fig. 5). In this geometry the active grating element corresponds to the fourth elementin SPR target with element width 9mm and period 18mm.The surface current measured using this target for h = 5mm amounted to 32 ± 5channels of CDC. So the registered shadowing effect is 64%. This effect is of considerableimportance to be taken into account in the calculation of SPR.308 G. A. NAUMENKO, A. P. POTYLITSYN, YU. A. POPOV and M. V. SHEVELEVFig. 3. – Scheme for measurement of the dependence on the impact parameter.Fig. 4. – Dependence on the impact parameter. Dots are the experimental points. Solid line isthe fit using (1).Fig. 5. – Scheme of shadowing measurement for the inclined grating element.EXPERIMENTAL TEST OF THE SHADOWING EFFECT IN SMITH-PURCELL RADIATION 309Fig. 6. – Scheme of shadowing measurement for the grating element parallel to the electronbeam.For another geometry shown in fig. 6, where the active surface is parallel to theelectron beam, the measured shadowing effect was inside of the experimental error (±7%).We may assert that no significant shadowing effect for this geometry is present.Finally we may conclude that the shadowing effect in SPR must be taken into accountin theoretical calculations depending on target geometry. Probably this is why a largediscrepancy between experimental results of SPR intensity and theoretical estimationswas observed in many works.∗ ∗ ∗This work was partly supported by the warrant-order 1.226.08 of the Ministry ofEducation and Science of the Russian Federation and by the Federal agency for scienceand innovation, contract 02.740.11.0245.REFERENCES[1] Naumenko G., Artru X., Potylitsyn A. et al., J. Phys.: Conf. Ser., 236 (2010)012004.[2] Artru X. and Ray C., Interferences between light emitted by charged particles crossingor skimming past optical fibers, in International Symposium RREPS’07, Prague, 2007.[3] Naumenko G. A., Potylitsin A. P., Sukhikh L. G. et al., JETP Lett., 90 (2009) 96.[4] Naumenko G., Artru X., Potylitsyn A., Popov Yu. and Sukhikh L., in Chargedand neutral particles channeling phenomena - Channeling 2008, Proceedings of the 51stWorkshop of the INFN Eloisatron project, edited by Dabagov S. B. and Palumbo L.(World Scientific) 2010, p. 511.[5] Naumenko G., Potylitsyn A., Popov et al., arXiv.org > physics > arXiv:0901.2630(2009).[6] Feinberg E L., Sov. Phys. Usp., 128 (1979) 539.[7] Shul’ga N. F. and Syshchenko V. V., J. Phys. At. Nucl., 63 (2000) 2018.[8] Potylitsyn A. P., Karataev P. V. and Naumenko G. A., Phys. Rev. E, 61 (2000)7040.[9] Naumenko G., Potylitsyn A., Popov Yu., Sukhikh L. and Shevelev M., J. Phys.:Conf. Ser., 236 (2010) 012024.310 G. A. NAUMENKO, A. P. POTYLITSYN, YU. A. POPOV and M. V. SHEVELEV[10] Naumenko G., Potylitsyn A., Popov Yu., and Sukhikh L., arXiv.org > physics >arXiv:0901.2732 (2009).[11] Brovnel J. H., Walsh J., Doucas G. et al., Phys. Rev. E, 57 (1998) 1075.[12] Sargsyan V., Comparison of Stripline and Cavity Beam Position Monitors, TESLAReport 03 (2004).

Experimental test of the shadowing effect in Smith-Purcell radiation

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Experimental test of the shadowing effect in Smith-Purcell radiation

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