FERMILAB-CONF-18-182-AD OPTICAL STOCHASTIC COOLING EXPERIMENT AT THE FERMILAB IOTA RING* J. D. Jarvis†, V. Lebedev, H. Piekarz, A. L. Romanov, J. Ruan, Fermi National Accelerator Laboratory, Batavia, IL 60510-5011, USA M. B. Andorf, P. Piot1, Northern Illinois University, Dekalb, IL 60115, USA 1also at Fermi National Accelerator Laboratory, Batavia, IL 60510-5011, USA Abstract Beam cooling enables an increase of peak and average luminosities and significantly expands the discovery po- tential of colliders; therefore, it is an indispensable com- ponent of any modern design. Optical Stochastic Cooling (OSC) is a high-bandwidth, beam-cooling technique that Figure 1: Simplified conceptual schematic of an optical will advance the present state-of-the-art, stochastic cool- stochastic cooling section. A wavepacket produced in the ing rate by more than three orders of magnitude. It is an pickup subsequently passes through transport optics and enabling technology for next-generation, discovery- an optical amplifier. In the kicker undulator, each particle science machines at the energy and intensity frontiers receives an energy kick proportional to its momentum including hadron and electron-ion colliders. This paper deviation. presents the status of our experimental effort to demon- strate OSC at the Integrable Optics Test Accelerator (IO- pass through a SC system. In practice, the spectral band- TA) ring, a testbed for advanced beam-physics concepts width, W, of the feedback system (pickup, amplifier, and technologies that is currently being commissioned at kicker) sets a Fourier-limited temporal response T~1/2W, Fermilab. Our recent efforts are centered on the develop- which is very large compared to the intra-particle spacing ment of an integrated design that is prepared for final and limits the achievable cooling rate. With a limited engineering and fabrication. The paper also presents a bandwidth on the order of several GHz, conventional SC comparison of theoretical calculations and numerical systems become ineffective for the high-density beams of simulations of the pickup-undulator radiation and its modern colliders. The realization of high-bandwidth/fast interaction with electrons in the kicker-undulator. cooling techniques, and their translation into operational systems, is a technological imperative for many future INTRODUCTION colliders. Beam cooling compresses a beam’s phase space by OPTICAL STOCHASTIC COOLING damping incoherent particle motions. It is a principal means of increasing achievable luminosity, preventing One possible solution is the extension of the SC princi- 14 emittance growth due to intra-beam scattering (IBS) and ple to optical frequencies (~10 Hz). This would in- other effects, reducing beam losses and improving energy crease cooling rates by three to four orders of magnitude, resolution; therefore, it is an indispensable component of and would be an extraordinary advance in beam-cooling any modern collider design. Beam cooling is an expan- technology. OSC was first suggested in the early 1990s sive area of research with many notable subfields, e.g. by Zolotorev, Zholents and Mikhailichenko, and replaced radiation, ionization, electron and stochastic cooling. the microwave hardware of SC with optical analogs, such Van der Meer’s Nobel-winning Stochastic Cooling as wigglers and optical amplifiers [7,8]. A number of (SC) was vital in the accumulation of antiprotons and in variations on the original OSC concept have been pro- the delivery of the beam quality required for the discovery posed, and its use has been suggested for hadron, heavy- of the W and Z bosons [1,2]. In SC and its variants, sig- ion, electron-ion and muon colliders and also controlling nals from electromagnetic pickups, operating in the mi- emittance growth in electron storage rings [9-15]. At crowave regime with a bandwidth on the order of several present, a proof-of-principle demonstration with protons GHz, are used in negative feedback systems to reduce the or heavy ions involves prohibitive costs, risks and techno- phase-space volume of a circulating beam in all degrees logical challenges [16]; however, demonstration of OSC of freedom [1-6]. with medium-energy electrons is a cost-effective alterna- If every beam particle’s deviation from the reference tive that enables detailed study of the beam-cooling phys- particle could be sensed and corrected individually, then ics, optical systems and diagnostics [17-20]. the total error in the beam could be removed in a single In the transit-time method of OSC, shown schematical- ___________________________________________ ly in Fig. 1 and upon which this program is based, a parti- * Fermi National Accelerator Laboratory is operated by Fermi Research cle’s deviations from the reference particle are encoded in Alliance, LLC under Contract No. DE-AC02-07CH11359 with the its arrival time at the kicker system by a magnetic bypass United States Department of Energy. [8]. The particle (an electron for purposes of discussion) † [email protected] first emits a radiation packet while traversing a pickup This document was prepared by [IOTA Collaboration] using the resources of the Fermi National Accelerator Laboratory (Fermilab), a U.S. Department of Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under Contract No. DE-AC02-07CH11359. undulator (PU), the wavelength of which is given by the an important diagnostic for temporal synchronization of usual (planar) undulator relation the light and particle optics. � �2 Cooling Rates and Ranges � = � �1+ + �2�2�, (1) � 2��2 2 The most critical parameters in OSC physics are the cooling rates and ranges for the longitudinal and trans- where λu is the undulator period, n is the harmonic num- verse phase planes. In the following analysis we use the ber, K is the undulator-strength parameter and θ is the usual generalized curvilinear definitions for coordinates observation angle relative to the beam axis. and derivatives, and we closely follow the analysis of The radiation packet is transported with (active) or reference [16]. In the interest of brevity, we enumerate without (passive) amplification to a kicker undulator only the salient steps and results. In the linear approxima- where it interacts with the same electron. Between the tion, a given electron is displaced longitudinally from the pickup and kicker, the electron traverses a bypass (chi- reference particle by cane), which is designed such that a reference particle at � Δ� the design energy will arrive at the kicker undulator sim- � = � � + � �′ + �� − ��� , (4) ultaneously with the head of its radiation packet. The 51 52 56 �2 � energy of the reference particle is unchanged by its inter- action with the radiation field in the kicker; however, in where (x,x’) is the transverse position and angle of the the linear approximation, all other particles will have a particle, Lpk is the pickup to kicker distance and M51, M52, delay that is proportional to their momentum deviation, M56 are the elements of the linear transfer matrix from the ∆p/p, and will receive corresponding corrective kicks exit of the pickup to the entrance of the kicker. The towards the design energy. transverse coordinates can be decomposed as betatron and In this arrangement, the magnitude of the momentum dispersive components as x=xβ+D∆p/p and x’= kick received by the particle in a single pass through the xβ’+D’∆p/p, where D and D’ are the dispersion and its cooling system is approximately derivative along the design orbit at the exit of the pickup. Neglecting betatron oscillations, we have �� ( ) = −� sin �0� (2) � Δ� Δ� � � = �� � + � �′ + � − ��� = � , (5) 51 52 56 �2 � �� � where k0=2π/λr and s is the longitudinal displacement of the particle relative to the reference particle after travers- and so for small s, the approximate cooling rate for the ing the bypass [16]. The gain parameter κ is given by longitudinal emittance is then � = √� Δ�/��, where G is the power gain of the optical amplifier and ∆E is the maximum energy exchange for a �� = �0��0���, (6) particle in the kicker. The form of ∆Ε can be estimated analytically by expressing the electric field via the where f0 is the revolution frequency in the ring. Redistri- Liénerd-Wiechert relation, and a modified Kirchhoff bution of the cooling between phase planes does not formula, and subsequently integrating against the motion change the sum of cooling rates [16,24]; it can be shown of a particle phased for maximum kick. This procedure that the horizontal cooling rate is then yields � � = � �� �� −� − ���. (7) � 0 0 56 �� �2 �� 2� �2 Δ� ≈ � � �2 �1+ �� (�, �� ) (3) 3� � 2 � � 0 � 2 -4 Neglecting Lpk/γ , which will be small in our case (<10 ), as the maximum energy exchange in the kicker without we see that the ratio of horizontal and longitudinal cool- ing rates for a given delay in the chicane is determined optical amplification. In equation (6), Nu is the number of entirely by the dispersion and its derivative at the exit of periods per undulator, and 0<fT <1 is a correction factor that accounts for longitudinal motions due to large values the pickup undulator as of K (>1) in the kicker and the finite collection angle of �� �56 the light optics, θm. It is interesting to note that for small = − 1. (8) �� ��� K and fT=1, Equation (6) is identical to twice the energy radiated, in the fundamental band, in a single undulator Coupling between the x and y dimensions can be provided [21]. This is the amount of radiation detected down- in the ring, outside of the cooling section, thus providing stream if the optical delay is detuned by more than the cooling in all degrees of freedom. duration of the wavepacket; sweeping the delay through In the case of a particle undergoing betatron oscilla- the wavepacket will produce coherent oscillations in the tions, we can parameterize the argument of equation (5) detected radiation of amplitude ~√� Δ� [22,23].