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High Aspect Ratio Electron Beam Generation in KEK-STF Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan) High Aspect Ratio Electron Beam Generation in KEK-STF M. Kuriki∗, ADSM/Hiroshima U., 1-3-1 Kagamiyama, Hgshiroshima,Hiroshima, 739-8530 H. Hayano, KEK, 1-1 Oho, Tsukuba, Ibaraki, 305-0801 S. Kashiwagi, REPS, Tohoku U., 1-2-1 Mikamine, Taihakuku, Sendai, 982-0826 Abstract of the beam energy and rapidly increased as a function of the beam energy. For example, in LEP accelerator[3] which Phase-space manipulation on the beam gives a way to is the last e+ and e- collider based on storage rings at this optimize the beam phase space distribution for a specific moment, the energy loss per turn was 2.1 GeV at 100 GeV purpose. It is realized by beam optics components which beam energy. If the energy is increased up to 250 GeV have couplings between degree of freedoms. In this article, which is required to measure Higgs self-coupling, the en- a high aspect ratio beam generation with a photo-cathode ergy loss becomes 72 GeV which can not be maintained at in a solenoid field is described. In International Linear Col- all. lider (ILC) project, a high aspect ratio electron beam is em- Linear collider concept has been proposed to break this ployed for high luminosity up to several 1034cm−2s−1 by difficulty. There is no fundamental limit on the energy for keeping “beam-beam effects” reasonably low. In the cur- linear colliders [7][8]. The acceleration is done by linear rent design of ILC, a high aspect ratio beam which corre- accelerators instead of Synchrotron. The energy is simply sponds to 250 in transverse emittance ratio, is generated by scaled with the total length of the linear accelerator and radiation damping in a 3km storage ring prior to the main accelerator gradient. On the other hand, eanch bunches acceleration. If such high aspect ratio beam is directly gen- passs through the interaction point (IP) only once due to erated from an injector linac, the 3km damping ring, a cou- the open topology. In a storage ring collider, each bunches ple of long transport lines, and a part of the bunching sec- pass through IP many times and the luminosity can be nat- tion can be omitted and the system becomes much simpler urally large. and cost-effective. We give a result of a simulation study The luminosity L of a collider is expressed as of the high aspect ratio beam generation. Here, we assume a test experiment in STF (Super conducting Test Facility) fn N 2 L = b , (1) in KEK. At last, an ILC design based on this method is 4πσxσy discussed. in case of gaussian beam profile. Here, f is pulse repeti- tion, nb is number of bunches in a pulse, N is number of INTRODUCTION particles in a bunch. We assume the same numbers of e+ and e-, respectively. σ and σ are transverse beam size E+ and e- collider (lepton collider) is a powerfull tool x y in horizontal and vertical direction. According to this for- for high energy particle physics. It reveals the hidden mula, L can be enhanced by decreasing the beam size. L symmetry of the nature by discovering verious new par- 0 is also enhanced by increasing f, n and N, but increasing tilces, resonance states, and weak-bosons, etc. Precise Z b these numbers make also power consumption large. studies[1] by SLC[2] and LEP[3] and CP violation mea- For a lepton linear collider, the small beam size at IP surements by B-factories[4] which had large impacts to es- is essential. On the other hand, the small spot size at IP tablish the standard model of particle physics. These ex- makes the beam current density quite high and enhances periments were carried out at the lepton colliders. After the beam-beam effect. The most serious effects among them big discovery of Higgs particle by LHC[5], a precise study is Beamstrahlung which is a synchrotron radition by mag- of Higgs particle property is strogly demanded and would netic field induced by the collison partner beam. By a sim- open a new era of modern physics[6]. Unfortunately, LHC ple consideration, the energy spread by this effect is is a proton-proton collider which is suitable for discovering a heavy mass particle, but not suitalble for any precise mea- ∆E N 2E (2) surement, because the initial state can not be determined 2 2 , E ∝ (σx + σy)σx well. In contrast, the initial state can be well defined in a lepton collider including the particle helicity. where ∆E is energy spread, E is beam energy , σz is lon- Due to the complemental property of the hadron collider gitudinal bunch length. An optimization to maximize L and the lepton collider, these two accelerators have been a and minimize ∆E/E is a high aspect ratio beam, i.e. a flat inseparable drinving force on the high energy physics. Un- beam. For example, if σx is kept at a reasonable value and fortunately, a lepton collider based on storage rings have σy is minimized, L can be enhanced inversely proportional a practical difficulty raising the beam energy beyond 100 to σy, but ∆E/E is increased only up to factor 2. GeV due to the huge synchrotron radiation energy loss . Table 1 shows the beam parameters of ILC at IP[8]. The The synchrotron energy loss is proporotional to 4th order aspect ratio in the transverse emittance is 250. In the cur- rent design, the high aspect ratio beam is generated by radi- ∗ [email protected] ation damping in a 3km storage ring. During the damping, - 410 - Proceedings of the 10th Annual Meeting of Particle Accelerator Society of Japan (August 3-5, 2013, Nagoya, Japan) One way to generate such correlation is using fringe field Table 1: Parameters of ILC IP of solenoid[9]. The fringe field of a solenoid at both ends Parameter Value are symmetric and the correlation made at the entrance is Horizontal beam size 640 nm cancelled at the exit, i.e. the beam passing through both Vertical beam size 5.7 nm ends does not have any correlation. To make the correla- Bunch length 300 µm tion, the beam should passes fringe field only at an end. If RMS energy spread by BS 2.4% the beam is generated in the solenoid field, the beam feels Horizontal n. emittance 10 mm.mrad only one fringe field. Vertial n. emittance 0.04 mm.mrad The vecotor potential of a solenoid field is given as B Ax = y, (8) − 2 there is a sub-effect that the bunch length becomes 9mm B which is not suitable for further RF acceleration. The beam A = x. (9) y 2 is then bunched down to 300 µm again after the damping. If the high aspect ratio beam is generated directly from We assume here no transverse momentum at the cathode an injector, we can omit the 3km storage ring and a part of surface. Because the canonical momentum is conseved, transverse momentum at the solenoid exit is bunch compressor. It makes the accelerator simpler and µ ¶ more costeffective. In this article, we discuss about the eB y P~ = , (10) high aspect ration beam generation from a photo-cathode in c 2 x a solenoid field. The simulation assumes a test experiment − at KEK-STF. At last, we discuss about a possible design of which gives Σ matrix as ILC employing this method. 1 0 0 κ 2 − 2 0 κ κ 0 Σ = r , (11) HIGH ASPECT RATIO BEAM 0 0 κ 1 0 κ 0 0 κ2 GENERATION BY MAGNETIZED BEAM − Phase-space distribution of particle beam is expressed where r is beam size in rms. The matrix has un-diagonal with sigma matrix. Here, we consider two dimensional components. It means that the beam has x-y correlation. space, x and y, four dimensional in phase space. In case The correlation made by the solenoid fringe field can be of no correlation between x and y, the sigma matrix is removed by series of skew-Q magnets. It consists from (at µ ¶ least) three skew-Q magnets represented by a matrix as σx0 0 −1 Σ0 = , (3) M = R Q(q3)O(d2)Q(q2)O(d1)Q(q1)R, (12) 0 σy0 where R is rotation matrix given as where σx0,y0 are nominal σ matrices for one dimensional µ ¶ 1 II case. From simpleticity, this Σ0 can be convereted to Σ1 R = , (13) √2 II with a simpletic transformation M as − µ ¶ where I is 2 2 unit matrix. Q(q) is a matrix of a nominal σx1 0 T × Σ1 = = MΣ0M , (4) quadrupole with gradient q and O(d) represents drift space 0 σ 1 y length d. Condition for removing the corelation is given by s where σx1,y1 are sigma matrices after the transformation. 2/eB + d1(d1 + d2)eB/2 From the simpleticity, matrix determinant should be con- q1 = , (14) stant as ± d1(d1 + d2)2/eB det(Σ0) = det(Σ1), (5) 2/eB q2 = − , (15) d1d2(1 + q12/eB) that leads q1 q2 eB/2 q3 = − − − . (16) det(σx0)det(σy0) = det(σx1)det(σy1), (6) 1 + d2d3q2(q1 + eB/2) These conditions are extracted as follows. In case of full and can be correlation, ~x0 and ~y0 vectors are in a relation of det(σx0) det(σx1) µ ¶ . (7) 2 det(σy0) ≪ det(σy1) 0 ~y0 = S ~x0 = eB ~x0.
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