LINEAR ACCELERATOR ACCELERATING MODULE TO SUPPRESS BACK-ACCELERATION OF FIELD-EMITTED PARTICLES

Abstract

A method for the suppression of upstream-directed field emission in RF accelerators. The method is not restricted to a certain number of cavity cells, but requires similar operating field levels in all cavities to efficiently annihilate the once accumulated energy. Such a field balance is desirable to minimize dynamic RF losses, but not necessarily achievable in reality depending on individual cavity performance, such as early Q.sub.0-drop or quench field. The method enables a significant energy reduction for upstream-directed electrons within a relatively short distance. As a result of the suppression of upstream-directed field emission, electrons will impact surfaces at rather low energies leading to reduction of dark current and less issues with heating and damage of accelerator components as well as radiation levels including neutron generation and thus radio-activation.

Claims

1. A method for suppressing prevalent field emission in the upstream direction in a radio frequency (RF) accelerator, comprising: providing an accelerator structure including plurality of cavities, a plurality of cells in each cavity, and an intermediate beam tube between the cavities; adjusting the beam length of the intermediate beam tube between the cavities according to the following equation $L_{\mathrm{tube}}=\left(N+\frac{1}{2}\right).Math.L_{\mathrm{cell}}\left(N+\frac{1}{2}\right).Math.\frac{.Math..Math.}{2}.$ wherein L.sub.tube is the beam length between cavities, L.sub.cell is the length of the cell cavity, is the particle velocity relative to the speed of light, is the wavelength of the accelerating mode, and N is an integer number; injecting a stream of electrons into said accelerator structure; and applying an accelerating field of at least 3 MV/m to accelerate the electrons to a relativistic speed.

2. An accelerator structure comprising: a plurality of cavities; a plurality of cells in each cavity; and an intermediate beam tube between the cavities; wherein the beam length of the intermediate beam tube between the cavities is adjusted according to the following equation $L_{\mathrm{tube}}=\left(N+\frac{1}{2}\right).Math.L_{\mathrm{cell}}\left(N+\frac{1}{2}\right).Math.\frac{.Math..Math.}{2}.$ wherein L.sub.tube is the beam length between cavities, L.sub.cell is the length of the cell cavity, is the particle velocity relative to the speed of light, is the wavelength of the accelerating mode, and N is an integer number;

Description

DESCRIPTION OF THE DRAWINGS

[0018] FIG. 1 depicts a possible impact energy range of electrons in an upgrade CEBAF cryomodule having eight seven-cell cavities, with all cavities operating at the nominal field level of E.sub.acc=19.2 MV/m totaling 108 MeV energy gain. The results are not fully mirror-symmetric due to numerically different start conditions.

[0019] FIG. 2 graphically depicts Normalized RF field amplitudes as a function of time for two adjacent cavities having different intermediate tube lengths, with the top graph depicting adjacent cavities with an intermediate tube length L.sub.tube=3.Math.L.sub.cell and the bottom graph depicting adjacent cavities with an intermediate tube length L.sub.tube=2.5.Math.L.sub.cell.

[0020] FIG. 3 is a schematic depicting electrons traveling through two five-cell cavities, which are phased to provide maximum energy gain for the main beam. The top schematic depicts electrons continuously field-emitted at the 1.sup.st iris of cavity 1 (C1 I1). The bottom schematic depicts electrons continuously field-emitted at the last iris of cavity 2 (C2 I6).

DETAILED DESCRIPTION

[0021] The present invention provides a practical method for suppressing FE in accelerating structures even in presence of field-emitting sites. Though important for SRF cavity cryomodules, the method applies generally to any type of RF accelerator. The benefit is a significant reduction of energy accumulation of upstream traveling field-emitted electrons, which mitigates dark current directed to the injector. The method is deemed most efficient for speed-of-light (=1) structures accounting for the fact that the electrons are swiftly accelerated to relativistic energies once captured by the RF field such that the travel distance per RF period is nearly equal to that of the main beam. The method is advantageous in that it does not require an alteration of the cavity design. The method includes adjusting the beam tube length (L.sub.tube) between cavities to obey:

[00002]$\begin{array}{cc}{L}_{\mathrm{tube}}=\left(N+\frac{1}{2}\right).Math.L_{\mathrm{cell}}\left(N+\frac{1}{2}\right).Math.\frac{.Math..Math.}{2}.& \left(2\right)\end{array}$

[0022] Herein L.sub.cell is the cavity cell length (/2, =wavelength of accelerating mode) and N is an integer number. L.sub.tube is often chosen to be 3.Math.L.sub.cell in SRF cavity cryomodules. This implies that RF fields in cavities oscillate synchronously at all times. The main beam accelerated in one cavity will then experience the same accelerating field after passage to the next cavity without phase adjustment (theoretically and assuming constant velocity). However, the RF phase can be technically tuned for each cavity depending on the tube length. The cavity interconnecting tube length cannot be chosen arbitrarily small, since it has to accommodate space for fundamental power couplers, pick-up probes for RF feedback control as well as HOM dampers and bellows depending on design requirements.

[0023] When applying the method, one also has to take into account isolation requirements between couplers of neighbouring cavities to avoid cross-talk effects that impede the low level RF control. This for instance concerns crosstalk between a power coupler of one cavity and the pick-up probe of the adjacent cavity or two power couplers facing each other. When using stainless steel bellows between cavities, the thermal losses in the bellows favour to place cavity flanges further away from the cavity cells. All the aforementioned considerations usually make N=0 and 1 impractical in SRF cryomodules. For N=2 (L.sub.tube=2.5.Math.L.sub.cell) however one obtains a reasonably long section for practical and thermal requirements, while saving cryomodule length and thus costs compared to 3.Math.L.sub.cell. Otherwise N=3 should be chosen.

[0024] FIG. 2 demonstrates the benefit considering two interconnected cavities for simplicity. It depicts the RF amplitude (normalized) in both cavities as a function of time when utilizing L.sub.tube=3.Math.L.sub.cell and L.sub.tube=2.5.Math.L.sub.cell, respectively. For L.sub.tube=3.Math.L.sub.cell there is no phase difference between the RF field amplitudes of the cavities (top plot). The main beam is represented by filled dots. The first bunch (leftmost filled dot) occupies one of the possible RF buckets at the chosen start time. At this moment one may imagine that the bunch center is in the mid of the last cell of the upstream cavity when the field just peaks (+1). This yields maximum acceleration downstream. After traveling a time corresponding to a length of L=L.sub.tube+L.sub.cell the bunch will pass the center of the 1.sup.st cell of the subsequent cavity (2.sup.nd filled dot) experiencing an accelerating field again (+1).

[0025] Field-emitted electrons moving downstream would be accelerated in the same way once efficiently captured by the RF assuming no significant phase slippage occurs. Electrons directed upstream will have to start when the field peaks in the opposite direction (1) corresponding to a 180 phase shift to the accelerating field in the same cell. Assuming this to be the time when field-emitted electrons arrive in the mid of the 1.sup.st cell in the downstream cavity (leftmost unfilled dot), these will reach the end cell of the upstream cavity when the field peaks again for further acceleration upstream (1 at 2.sup.nd unfilled dot). Consequently in this case (L.sub.tube=N.Math.L.sub.cell), electrons may accumulate the same energy gain whether directed up- or downstream.

[0026] Referring to the bottom plot of FIG. 2, for the case when L.sub.tube=2.5.Math.L.sub.cell the RF phase of the downstream cavity (dashed curve) has to be adjusted in order to be synchronous with the main beam (filled dots). This requires a relative RF phase shift of 90 with respect to the upstream cavity (solid curve). Field-emitted electrons directed downstream would still experience energy accumulation as in the former case. However, field-emitted electrons originating in the downstream cavity will have to start when the field peaks in opposite direction (1). If we assume the 1.sup.st unfilled dot (leftmost) corresponds to the time the electrons are located in the center of the 1.sup.st cell of the downstream cavitynot restricting generalitythen by the time the electrons travel to the end cell of the upstream cavity the RF field will be decelerating (+1). Therefore, field-emitted electrons directed upstream in the way described above will lose all the energy accumulated previously.

[0027] Note that in reality field-emitted electrons are emitted during a finite phase range. This causes differing trajectories and energy spread among particles. Perfect energy annihilation cannot be achieved for all possible trajectories.

[0028] Trajectories also depend on the specific cavity shape. The proposed method however provides a significant reduction of upstream energies in all conceivable cases when obeying equation (2).

[0029] FIG. 3 illustrates two numerical case studies for a string of two five-cell cavities. The difference is only the initial FE region. In both cases electrons are seeded into the RF volume according to the Fowler Nordheim equation covering several RF cycles sufficient for electrons to pass the full string. It allows electron bunches being emitted over a relatively wide phase space at times when the field peaks. The shading intensity within the cavities corresponds to the electron energy as denoted in the legends. The cavity interconnecting tube length is L.sub.tube=2.5.1.Math..sub.cell The RF frequency is 1.5 GHz yielding an active length of 0.5 m for a single cavity. Both cavities are operating at E.sub.acc=12.5 MV/m corresponding to 6.25 MeV energy gain per cavity. The cavities in both cases are phased such that a main bunched beam at 0=1 would experience the maximum energy gain of 12.5 MeV passing both cavities. In the upper plot the field-emitters symmetrically occupy the region around the 1.sup.st iris of cavity 1 upstream (C1 I1). Here, those electrons captured close to the beam axis experience an energy gain of 11.6 MeV at the exit of cavity 2, slightly short of the 12.5 MeV feasible, which is a consequence of the particles emitted only with a few eV at the surface. In the bottom plot the seeding site is around the last iris of cavity 2 (C2 I6). Now only cavity 2 provides ideal conditions for acceleration in upstream direction with the maximum energy reached within the beam tube, whereas cavity 1 decelerates the beam. Some electrons come to almost a complete stop at the exit of cavity 1 (upstream) and present the least harm with regard to electron loading effects. This is in principle agreement with the simplified analytical approach depicted in FIG. 2. Some electrons initially dragging behind the leading particles however can exhibit a large phase slippage and are therefore not as efficiently decelerated. These may accumulate a few MeV energy again within cavity 1, which is yet significantly lower than in case of L.sub.tube=N.Math.L.sub.cell. Furthermore, the maximum energy accumulated is likely to decrease in a longer chain of cavities for the same particles as long as L.sub.tube=(N+).Math.L.sub.cell.

[0030] Although the description above contains many specific descriptions, materials, and dimensions, these should not be construed as limiting the scope of the invention but as merely providing illustrations of some of the presently preferred embodiments of this invention. Thus the scope of the invention should be determined by the appended claims and their legal equivalents, rather than by the examples given.