Investigations of the concept of a multibunch dielectric wakefield accelerator

Investigations of the concept of a multibunch dielectric wakefield accelerator

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Investigations of the concept of a multibunch dielectric wakefield accelerator I.N. Onishchenko, V.A. Kiselev, A.F. Linnik, V.I. Pristupa, G.V. Sotnikov NSC Kharkov Institute of Physics and Technology, Kharkov, Ukraine

art ic l e i nf o

a b s t r a c t

Article history: Received 26 November 2015 Received in revised form 9 February 2016 Accepted 21 February 2016

Theoretical and experimental investigations of the physical principles of multibunch dielectric wakefield accelerator concept based on the wakefield excitation in the dielectric structure by a sequence of relativistic electron bunches are presented. The purpose of the concept is to enhance the wakefield intensity by means of the multibunch coherent excitation and wakefield accumulation in a resonator. The acceleration of bunches is achieved at detuning of bunch repetition frequency relative to the frequency of the excited wakefield. In such a way the sequence of bunches is divided into exciting and accelerated parts due to displacing bunches into accelerating phases of wakefield excited by a previous part of bunches of the same sequence. Besides the change of the permittivity and loss tangent of dielectrics under the irradiation by 100 MeV electron beam is studied. & 2016 Elsevier B.V. All rights reserved.

Keywords: Wakefield excitation Dielectric structure Sequence of bunches Electron acceleration

1. Introduction The present high-energy frontier lepton colliders producing the center-of-mass energy of 100 GeV [1] give the possibility to study the world of nature of which the size can be seen into nearly onetrillionth micron. Today we are launching forth into a new energy regime of the order of TeV [2,3], in which profound fundamental questions are expected to be answered on the origin of mass, the predominance of matter over antimatter and the existence of supersymmetry. However CLIC and ILCscale accelerators [2,3] are very close to the limit [4] of what we can practically afford to build using conventional technologies, even collaboratively. The first understanding of this situation was stated in [5], where three new ideas of particle acceleration were declared. The only Fainberg proposal to use of plasma waveguides as accelerating structures has survived and was later modified by Dawson et al. [6,7] as a wakefield accelerating scheme, in which high-gradient accelerating field is built up as a wakefield excited in plasma by a short high power laser pulse or a short bunch of the large charge. Another potential candidate for future high gradient particle acceleration, allowing to overcome the accelerating rate limit 100 MeV/m of conventional accelerators, is dielectric loaded (DL) accelerating structures [8], in which wakefield is excited by an intense electron bunch or a sequence of bunches. As it has been shown in theoretical investigations [9] and in the recent experiments [10], the maximum accelerating gradient in dielectric structures, being limited by the electric breakdown due to the tunneling and collisional ionization effects, can be achieved above E-mail address: [email protected] (I.N. Onishchenko).

1 GeV/m, i.e. on the order higher compared to the conventional metallic accelerating structures. Besides, DL structures are more acceptable due to the developed technology of microfabrication, homogeneity, microwave matching, etc. In this work the concept of multibunch dielectric wakefield accelerator is investigated [11,12]. The theoretical and experimental studies of the following problems are carried out:

 “multibunch” issue that is concluded to the wakefield 





enhancement due to the summation of coherent wakefields driven by a periodic sequence of electron bunches; “resonator” issue that is concluded to the wakefield enhancement by using a resonator to avoid the effect of group velocity so that the energy of excited wakefield does not vacate the dielectric structure during the wakefield excitation by all bunches of the sequence; injection problem that is concluded to displacing rear tail of the sequence of bunches into accelerating phases of the wakefield by means of detuning bunch repetition frequency and excited wakefield frequency; influence of exposure to relativistic electron beam on radiation resistance and electrodynamic properties of dielectrics.

2. Wakefield excitation As a result of works on the restoration of the klystron amplifier, update the electron gun and master oscillator, which were performed at linear resonant electron accelerator “Almaz-2M”, the relativistic electron beam, which energy can be varied in the range

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2.5–4.8 MeV, pulsed current 0.5–1.0 A, pulse duration 0.1–2.0 μs. Beam pulse presents a sequence of N ¼300–6000 electron bunches each of charge within 0.16–0.32 nC, radius 0.5 cm, duration 60 ps (i.e. length 1.7 cm) and interval between bunches 300 ps (at bunch repetition frequency frep ¼2805 MHz). Bunch repetition frequency can be changed within 2803– 2807 MHz. Energy distribution width is within 7-9-%. A chamber in which the dielectric structure can be placed was attached to the accelerator “Almaz-2”. In such a way the experimental facility has been created for research of wakefield excitation by a sequence of the relativistic electron bunches in the dielectric structures of round and rectangular cross-section and acceleration of electrons by excited wakefields. The scheme of the experimental set up is shown in Fig. 1. The dielectric structure was a copper cylindrical waveguide (5) of the inner diameter of 85 mm, filled with annual Teflon tube (4) ðε ¼ 2:04; tg δ ¼ 2  10  4 Þ of the outer diameter equal to the inner diameter of the copper waveguide and transit channel of the diameter 2.1 cm for bunches propagation. The length of the dielectric part is 31.8 cm equal to 3 wavelengths of the principal mode. Electron energy spectra were measured by a magnetic analyzer (2) at the accelerator exit and by declining electrons with transversal magnetic field (6) on glass plate (10) at the dielectric structure exit. 2.1. “Multibunch” excitation “Multi-bunch” issue concluded to the statement that the intense wake field excited by a bunch with a large charge can be achieved by a long periodic sequence of bunches with a low charge each, but with an equivalent total charge. To clarify the possibility of coherent summation of individual bunches fields it is needed to change the number of bunches in the sequence. Because of the difficulty of producing a set of sequences with various number of bunches in the performed studies waveguides of various length were used. The possibility of such a substitution follows from the fact that due to the output of the excited wave from the waveguide of finite length with the group velocity vg the number of bunches of the sequence of any duration which contributes to the growth of the total wakefield at the waveguide exit is limited. Maximum number of bunches N max , which wakefields during coherent summation increase the amplitude of the total field, is directly proportional to the length of the dielectric waveguide Ld : N max ¼ 1 þ Ld =λðv0 =vg  1ÞÞ, where λ is length of the excited wave equal to the distance between the bunches, v0 is the bunch velocity. So, in spite of a long sequence of bunches (up to N ¼6000 bunches) we can observe the wakefield signal at dielectric waveguide exit from 1,2,3… bunches by means of changing dielectric waveguide length Ld. The dependence of the excited field at dielectric waveguide output on time for the two waveguide length L ¼ λ=4 and L ¼ λ=2 and vg ¼ v0 =2 is shown in Fig. 2(a) and (b). It can be seen that the amplitude of the wakefield does not change for L o λ.

With the further increase in the length of the waveguide the excited wakefield amplitude is growing stepwise by each length λ. (Figs. 2(c), (d) and 3). To account the transition radiation, which inevitably occurs on electrodynamic jumps in real structures, and reflections of excited fields in imperfectly matched waveguides, the model (Fig. 4) close to the experiment was taken for simulation of the wakefield excitation in the dielectric waveguide by a sequence of bunches. Into a metal cylindrical waveguide of length Ls the dielectric part of length Ld is inserted. Electron bunches propagate along a cylinder axis from left to right. Fig. 5 shows the dependence of obtained the total excited field on the dielectric structure length. Existence of maxima and minima on curves of dependence of a wakefield from length of the dielectric plug is connected with two factors. Firstly, when dielectric lengths are multiple to a half of wavelength of a resonant mode the reflection of a wave excited by a bunch on a dielectricvacuum boundary is minimum. Such behavior is similar to passing of plane wave through a dielectric plate. Secondly, the partially reflected wave is coherently added with a direct wave, and the full field grows in a segment of dielectric tube that will lead to increasing of the radiated field in case of the subsequent falling of a wave on boundary of the section of mediums. The situation with growth of a field is similar to accumulation of energy in the resonator. The experimentally obtained linear growth of the total wakefield excited in the dielectric waveguide by a long sequence of 6  103 bunches (each of charge 0.26 nC and duration of 60 ps, and bunch repetition frequency 2805 MHz) upon the variable length of the dielectric waveguide (0–35 cm, step 2.5 cm), evidencing the coherent addition of wakefields of the bunches, which fields overlap with increasing of the waveguide length. By such a method the measurement of the values of wakefield excited by 1, 2, 3 and 4 bunches by changing waveguide length Ld was carried out. Fig. 6 shows the obtained dependence of wakefield amplitude on the dielectric waveguide length. It is similar to the dependence obtained in the simulation (Fig. 5). In the case of rectangular waveguide with two dielectric plates there is the possibility to make the same influence of reflections for various interaction length of bunches with dielectric part of the waveguide. For this aim electron bunches should be deflected on the walls free of dielectric plates by magnetic field of movable permanent magnet. So the measurements were carried out at the same length of the whole dielectric waveguide avoiding changes in the conditions of reflections when varying the interaction length. In this experiment the wakefield amplitude at the dielectric waveguide exit linearly depends on the interaction length of bunches with dielectric part (Fig. 7). It confirms more distinctly the coherent summation of wakefields of individual bunches comparatively to the case of the cylindrical waveguide (Fig. 6).

Fig. 1. The scheme of the experimental setup. 1 – accelerator “Almaz-2”, 2 – magnetic analyzer, 3 – diaphragm, 4 – dielectric structure, 5 – metal waveguide, 6 – traversal magnetic field, 7 – vacuum Teflon plug, 8 – microwave probe, 9 – oscilloscope, 10 – glass plate, and 11 – waveguide with a horn.

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Fig. 2. Dependence of the longitudinal wakefield on time at the exit of the dielectric waveguide of various lengths: a  L ¼ λ=4; b  L ¼ λ=2; c  L ¼ λ; d  L ¼ 2λ. Number of bunches N ¼ 10.

Fig. 3. Dependence of the longitudinal wakefield amplitude at the waveguide exit on waveguide length.

2.2. “Resonator” scheme of excitation The aim of the “resonator” concept is, firstly, to increase the number of bunches of the sequence, adding wakefields of which increases the total wakefield in comparison with the case of a waveguide case, and, secondly, to increase the amplitude of the total wakefield by adding fields of excited equidistant (hence resonant) modes. In the resonator concept all bunches of the sequence contribute to the increase in the wakefield amplitude, which grows proportionally to the total number of bunches Nb. In this case, coherent energy losses of the bunch grow with its number, and the total energy loss of the whole sequence is proportional to N 2b . In the resonator with quality factor Q ¼ 1 all bunches of the long sequence increase the total wakefield in the resonator. In the absence of losses in the resonator and the multiplicity of frequencies of transverse modes (i.e. their equidistance), declared conditions should provide coherent summation of wakefield of all

Fig. 4. Model for simulation of wakefield excitation in the dielectric structure by a sequence of electron bunches.

bunches and all excited transverse modes, and thereby increase the total wakefield to the level of field, excited by a single bunch with a charge equivalent to the total charge of all bunches of the sequence. The amplitude of the total wakefield (accordingly, the number of bunches, contributing to the field increase) is limited by the finite quality factor Q. For finite Q-factor the dependence of the total wakefield upon the duration of a sequence of bunches experimentally investigated using the cylindrical compoundresonator, consisting of a dielectric part of length L1 ¼ 3λ, λ ¼ 10:6 cm is the wavelength in dielectric part, filled with Teflon ðε ¼ 2:04; tg δ ¼ 2  10  4 Þ, with the transit channel of diameter 21 mm and of a vacuum part of length L2 ¼ λv =2, and diameter 85 mm, λv ¼ 39 cm is the wavelength in vacuum part. Wakefield is

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Fig. 5. Simulated dependence of Ez amplitude of wakefield on the dielectric part length.

Fig. 8. Dependence of the wakefield amplitude on the duration of bunch sequence for various Q-factors of the compound-resonator: 1 – Q 1 ¼ 65, 2 – Q 2 ¼ 268, 3 – Q 3 ¼ 539, 4 – Q 4 ¼ 676.

Fig. 6. Dependence of Ez amplitude of excited wakefield on the matched dielectric waveguide length.

Fig. 7. Dependence of wakefield amplitude on interaction length of bunches with dielectric waveguide.

excited by a sequence of 6  103 4.5 MeV electron bunches each with charge of 0.26 nC, diameter of 1 cm and duration of 60 ps. The experimentally measured dependences of the total wakefield upon the duration of a sequence of bunches for various Qfactors of the compound-resonator are shown in Fig. 8. It is seen that with increasing duration of the sequence the total field increases and saturates, remaining constant for larger durations. With the growth of the Q-factor the number of bunches of the sequence contributing to the increase in the total wakefield increases. The long sequence of 6  103 bunches in our experiment is practically equivalent by saturation amplitude to the sequence of infinite number of bunches. At Q¼676 of the cylindrical compound-resonator the measured value of wakefield in the vacuum part is Ezv ¼ 24 kV=cm that corresponds to Ezd ¼ 11:8 kV=cm in the transit channel of the

dielectric part. For the case of waveguide length Ld ¼ 3λ wakefield amplitude was only 1 kV/cm (see Fig. 6). The wakefield excitation by a sequence of bunches in multimode (thick plates t ¼15.3 mm) quartz ðε ¼ 3:75; tg δ ¼ 10  4 Þ rectangular resonator showed that wakefield increase to Ezd ¼ 7 kV=cm, 12 times higher in comparison with the case of the waveguide, due to the wakefield summation of larger number of bunches. Expected amplitude “peaking” and increasing principal mode amplitude caused by the addition of transverse modes in the waveguide case at the excitation by a single bunch, in the experiment with a resonator of rectangular (the same for circular) cross-section and a long sequence of bunches were not observed. This result is explained by the fact that transverse modes, except the principal one, are nonresonant. As a result, the total wakefield is monochromatic. The wakefield excitation by the sequence bunches in the single-mode (thin plates t ¼4.7 mm) quartz resonator of rectangular cross-section at the double frequency f 0 ¼ 2f rep was performed. The excitation of monochromatic wakefield with amplitude Ezd ¼ 2:8 kV=cm was realized. Monochromaticity in this case follows from the fact that in the appropriate waveguide case one bunch excites mainly one mode at the frequency f 0 ¼ 2f rep , with which coupling coefficient is maximal. Other modes are almost not excited. The experiment with such resonator showed the excitation monochromatic wakefield increased 9 times compared to the waveguide case due to more number of bunches which wakefields contribute to the total field. The wakefield excitation by a sequence of bunches in multimode zirconia dielectric ðε ¼ 23; tg δ ¼ 10  3 Þ rectangular resonator was carried out too. At resonant conditions prevailing excitation of principal mode to the level 200 V/cm was observed. Such low level is caused by a large loss tangent. It demonstrated the presence of excited second radial mode at a frequency 6.7 GHz in the resonator of the cylindrical geometry and the frequencies of several transverse modes for a rectangular geometry, whose contribution to the total wake field is not

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essential unlike to the case of the waveguide. The reason of this inessentiality, which does not allow enhancing the total wakefield, is nonmultiplicity of the mode frequencies to the principal mode frequency and therefore not getting into the resonance with bunch repetition frequency and eigenfrequency of the resonator.

3. Injection problem for acceleration of bunches To solve the “injection” problem using introducing detuning between bunch repetition frequency and frequency of excited wakefield, that allows obtaining driving and accelerated bunches from the same sequence. For the case of introduced detuning the theoretical and experimental studies of the wakefield excitation in the dielectric waveguide/resonator by a part of electron bunchesdrivers of a periodic sequence and the acceleration by this wakefield of the other part of the bunches-witnesses of the same sequence. Such situation becomes possible due to successive shift of bunches by phase of excited wakefield. In the performed experiments the frequency of dielectric wakefield is fixed and determined by the Cherenkov resonance (coincidence of the velocity of bunches and the phase velocity of the excited wave of the dielectric waveguide). The bunch repetition frequency is varied by change of the frequency of master oscillator “Rubin” of klystron amplifier. In this concept of “excitation-acceleration” by using the same sequence of bunches there is no need in additional linac injector for producing bunches-witnesses, which simplifies the experimental demonstration of bunches acceleration by the excited wakefield. In the case of resonance, i.e. coincidence of bunch repetition frequency frep and frequency of the principal mode of excited wakefield f0, all bunches are occurred in the decelerating phase and lose energy to excite wakefield. In the presence of frequency detuning Δf ¼ f rep f 0 a 0 bunches of the first part of the sequence occurred in the decelerating phases of excited field lose energy to the increase in total wakefield and bunches of the next part of the sequence, shifted to the region of the accelerating phases of wakefield excited by the previous part of the sequence, gain an additional energy. For point and monoenergetic bunches the number of bunches Nn of the first part of the sequence, exciting wakefield, can be evaluated from the condition of phase shift on pi Nn th bunch N n ¼ f rep =2Δf . The next part of the sequence of bunches of the same duration is accelerated. Calculated electron energy spectra for initial monoenergetic bunches in the single-mode approximation for the cases of infinitely thin ring bunches (1) and bunches with rectangular longitudinal and transverse profiles (2) are shown in Fig. 9. Electron 2 energy is normalized pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiby W ¼ mc γ , where γ is the relativistic factor, γ ¼ 1= 1  v2 =c2 . Following parameters of the dielectric waveguide and the sequence of electron bunches are taken: radius of the metal tube is b¼ 4.325 cm, radius of the transit channel is a ¼1.44 cm, dielectric constant is ε ¼ 2:1, radius of the bunches is rb=a ¼ 0:5, number of bunches in the sequence is N ¼ 500, charge of bunch is Q¼0.32 nC, detuning value is Δf =f rep ¼ 0:002, τb f 0 ¼ 0; 1=6 is the duration of a single bunch. It is seen that in the case of an infinitely thin ring bunches ðr ¼ r b ; τb f 0 ¼ 0Þ energy spectrum of interacted bunches has two narrow maxima (1) corresponding to the accelerated and decelerated bunches. Maximal increase of the relativistic factor is Δγ ¼ 0:9 or 410 keV for the initial energy 4.5 MeV. For bunches with rectangular longitudinal and transverse profile ðr ¼ 0  r b ; τb f 0 ¼ 0  1=6Þ broadening of the energy spectrum is essential (2). Instead of narrow peaks two poorly defined maxima occurred. More broadening of the energy spectrum is caused by existence of

Fig. 9. Electron energy spectra for a sequence of 500 infinitely thin ring bunches (1) and bunches with rectangular profile (2) at detuning Δf =f rep ¼ 0:002.

accelerating (decelerating) wakefield gradient inside the electron bunches. Let us take into account also existing in the experiment the initial electron energy spread of the bunch, which is described by a pffiffiffiffi model distribution function F 0 ¼ ð1= π Δγ Þexp  ðγ  γ 0 Þ2 =Δγ 2 , where Δγ is the characteristic spread of relativistic factor γ and γ0 is its averaged value. We consider injection of a sequence of relativistic electron bunches into dielectric resonator without losses ðQ ¼ 1Þ in the presence of detuning between the bunch repetition frequency and wakefield frequency. In Fig. 10 the electron energy spectra before (solid line) and after (dash line) interaction for initial energy spread Δγ ¼ 0:5 and number of bunches N ¼1000 are presented for the resonance case (Fig. 10a) and for the case of detuning (Fig. 10b). It can be seen that for the resonant case Δf =f rep ¼ 0 the distribution function is shifted to the left as a whole, i.e. all electrons lose their energy for wakefield excitation. For the case of detuning Δf =f rep ¼ 0:001 distribution function broadening caused by deceleration and acceleration of electron bunches takes place. Maximized Increase of energy in this case is about 175 keV. Fig. 11(a) and (b) shows experimentally obtained energy spectra of the electrons of the beam passing through the resonator without dielectric (1) and through the resonator with dielectric (2), i.e. without and with Cerenkov interaction of bunches with excited wakefield. Fig. 11a demonstrates resonant case, when detuning Δf ¼ 0. Fig. 11b demonstrates nonresonant case, when detuning Δf ¼ 2:5 MHz. Note that the initial spectra (without dielectric) are normalized by I=I max . Spectra after interaction are presented in the units of normalized initial spectra providing the conservation of full number of particles. It allows to judge about the quantity of accelerated and decelerated particles. From Fig. 11 it follows that in the presence of dielectric in the case of resonance Δf ¼ 0 the energy spectrum is shifted by 400 keV as a whole to lower energies that is caused by the energy loss of all the bunches on the wakefield excitation. In the case of detuning between the bunch repetition frequency and the frequency of wakefield Δf ¼ f rep  f 0 ¼ 2:5 MHz a part of bunches of the sequence, shifting over phase, falls into the accelerating phase of the wakefield excited by previous bunches of the same sequence and gain energy. In this case, in the electron energy spectrum both the electrons losing energy (  150 keV) and electrons gaining additional energy ( þ150 keV) are observed.

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Fig. 10. Initial electron energy spectra (solid line) and final electron energy spectra (dash line): Δf =f rep ¼ 0; b  Δf =f rep ¼ 0:001.

4. Change of dielectric and mechanical properties under electron beam irradiation Irradiation of samples made from zirconium ceramics (ZrO2– 4 wt% MgO) was carried out by using electron linac LUE-40 with electron beam energy up to 100 MeV [13]. There were 20 samples in the form of discs irradiated with different fluences of the electron beam (from 2  1016 cm  2 to 2  1018 cm  2) and the energy of the particles up to 90 MeV. The change in temperature of samples during irradiation did not exceed 100 °C. Studies of the irradiated samples allowed obtaining the information about induced activity and changes in the electrodynamical and mechanical properties of zirconium ceramics. A measurement of change of the dielectric properties of ceramic samples with a diameter of 10 mm and thickness of 2.5 mm was carried out by using the resonator method with a partial/full filling RF cavity. The irradiation exposure in this case was 16.5 h to obtain fluence 2  1018 cm  2. Comparison of the resonant frequency and Q-factor of resonators before and after irradiation showed the following:

 Permittivity is reduced by ð0:23 7 0:02Þ%.  Loss tangent is not changed within range 7 3%. To investigate the influence of electron irradiation on the mechanical properties of zirconium ceramics two samples ZrO2– 4 wt% MgO with diameter of 10 mm were selected. The first one was irradiated by electron beam with energy of 45 MeV and the second one was irradiated by electron beam with energy of 89 MeV. The fluence was 2  1016 cm  2 obtained during 0.5 h exposure. Studies of the samples showed that irradiation leads to phase transitions in the structure of the dielectric, and to phase transformation of cubic zirconia. In the grains under irradiation by the electron beam with energy of 45 MeV the formation of lensshaped grains of tetragonal phase took place. With increasing electron beam energy to 89 MeV these grains grow and turn into

Fig. 11. Energy spectra of electron bunches passing through the resonator without dielectric (1) and a resonator with dielectric tube (2):  Δf ¼ 0; b  Δf ¼ f rep  f 0 ¼ 2:5 Hz.

crystals of lamellar shape. These changes in the structure of the zirconium ceramics lead to the formation of a composite structure. At that the fragility of the material is decreased and hardness is decreased from 12.2 to 10.8 and 10.5 GPa after irradiation of the ceramic material by the electron beam with energy 45 and 89 MeV, respectively. The Vickers hardness of the material and fracture toughness was measured by indentation technique on TP7 hardness meter.

5. Conclusion The possibility of wakefield amplitude enhancing in “multibunch” and “resonator” regimes of the excitation is theoretically and experimentally investigated. It is shown that the coherence at coincidence of bunch repetition frequency and excited wakefield frequency in “multibunch” regime and the accumulation of wakefields at multiplicity of eigenfrequencies of the resonator to the bunch repetition frequency and excited wakefield frequencies in “resonator” regime provides enhancement of the total wakefield. Impossibility to realize coincidence/multiplicity of mentioned frequencies with Cherenkov resonance frequencies of transverse modes because of their nonequidistance causes insufficiently effective enhancing of the total wakefield amplitude. The acceleration of bunches in wakefield excited by bunches of the same sequence at introduction of detuning between bunch

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repetition frequency and excited wakefield frequency is demonstrated. It is determined that the irradiation of samples made from zirconium ceramics (ZrO2–4 wt% MgO) by 90 MeV electron beam with fluence of order 1018 m  2 changes the dielectric permittivity by 0.23% that is sufficient to destroy the conditions of Cherenkov resonance in the acceleration process. Mechanical properties of zirconium ceramics are changed too. Fragility is decreased and hardness is reduced.

Acknowledgment This work is supported by Global Initiatives for Proliferation Prevention (GIPP) Program; Project ANL-T2-247-UA (STCU Agreement P522).

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