Longitudinal Phase Space Research Articles

Beam stacking experiments at the ion accumulation ring TARN

The ion beam accumulation ring TARN was constructed at INS in 1979. In this ring the combination of multiturn injection and rf stacking has been employed to store the beam in the horizontal betatron and in the longitudinal synchrotron phase space. In the experiments, twenty turns of beam were injected into a betatron phase space area of 153 π mm mrad, and about 20 pulses were stacked in the synchrotron phase space area with a fractional momentum spread, ΔP/ P, of 2.3%. An overall stacking number of about 300 turns was attained. The repetition rate of the rf stacking was 30 Hz and it required approximately 0.5 s to fill the four-dimensional phase space area with beam. In the present paper, the results of the beam accumulation experiments are given and then compared with those of computer simulations.

Semi-Inclusive Rapidity Distributions from a Longitudinal Phase Space

Single particle rapidity distributions in events with fixed multiplicities are calculated using a longitudinal phase space model with a constant transverse momentum. Two cases (1) pion-pion collisions with no leading pions (or e+-eannihilation into pions) and (2) nucleon-nucleon collisions with leading nucleons are considered and numerical results are given for the c.m. total energy W =540 GeV. In Case (1), sharp peaks appear at the ends of the available rapidity space when the multiplicity n is less than 13 while the peaks disappear and a fiat plateau develops when 15:S n:S 60. The plateau changes into a smooth bump as n increases further. In Case (2), both peaks at low n and a plateau at medium n are smeared out considerably by the leading particle effect, and a smooth bump dominates for almost all range of n. Prominent dips observed experimentally in the pseudorapidity distributions for low n are not reproduced in the calculated rapidity distributions.

Optical characteristics of the KSU superconducting linac

The J. R. Macdonald Laboratory at Kansas State University is now constructing a superconducting linac to be used for investigating ion collision physics. These atomic physics experiments call for ion beams with high charge states and a wide range of projectile velocities. To provide such beams, the linac will act as both an accelerator and as a decelerator of beams injected from an EN tandem. Preliminary studies of the longitudinal and transverse phase spaces of these beams are discussed, and projected beam characteristics are reported for several ions. Special attention is given to the characteristics and problems of deceleration.

Increased Intensity Performance of the Brookhaven AGS

With the advent of H- injection into the Brookhaven AGS, circulating beams of up to 3 × 1013 protons at 200 MeV have been obtained. Rf capture of 2.2 × 1013 and acceleration of 1.73 × 1013 up to the transition energy (? 8 GeV) and 1.64 × 1013 to full energy (? 29 GeV) has been achieved. This represents a 50% increase over the best performance obtained with H+ injection. The increase in circulation beam current is obtained without filling the horizontal aperture. This allows the rf capture process to utilize a larger longitudinal phase space area (? 1 eV sec/bunch vs ? 0.6 eV sec with H+ operation). The resulting reduction in relative longitudinal density partially offsets the increase in space charge effects at higher currents. In order to make the capture process independent of injected beam current, a dynamic beam loading compensation loop was installed on the AGS rf system. This is the only addition to the synchrotron itself that was required to reach the new intensity records. A discussion of injection, the rf capture process, and space charge effects is presented.

Stochastic Momentum Cooling of a Low Energy Beam at TARN

storage ring which accumulates the beam both in the longitudinal and transverse phase spaces from the injector sector focusing cyclotron. This storage ring has been mainly used to develop the accelerator technology related to the future project of high energy ion accelerator at INS. Details of the pe;formance of beam accumulation are presented elsewhere. In the meanwhile the stochastic momentum cooling has been also performed in this ring for the low energy 7 MeV/u RF stacked protons and c( particles in view of future application of such a technique to the cooler ring for the study of precise nuclear and atomic physics experiments. The stochastic cooling of a low energy beam has been successfully tried at LEAR, CERN where they cool antiprotons, such as 50 or 175 MeV. However recently still lower energy beam, for example 5 MsV, is required for the nuclear experiments with nearly stopped antiprotons. In contrast with high energy beam cooling, two major experimental conditions should be attained. Firstly the beam life due to the residual gas scattering should be much longer than the cooling time. At the average pressure of around lo-l1 Torr, the beam life of protons and a. particles are several thousands seconds which is one order larger than the present cooling time of several hundreds seconds. Secondly the special attention should be paid to obtain the high coupling and high shunt impedance of the pickup and kicker as the particle's velocity is as low as 12 % of the light velocity. In the present experiment a travelling wave type coupler with a helical inner conductor has been used with a sufficient performance. The cooling system including these couplers and a notch filter operates successfully, and experiments have been carried out to measure cooling time, final momentum spread, etc. by varying system gain and signal's transmission time. For the analysis of experimental data, we improved the Sa;h;rer's formulation of a Fokker-Planck equation. ' In the improvement, coherent correction of particle energy is expressed explicitly in terms of the difference of particle-signal's transmission time from time-of-flight of the particle. This paper describes the experimental results on cooling time, final momentum spread, etc., in compared with our theory. The hardware of the cooling system is presented elsewhere.5

Numerical Studies of High Current Beam Compression in Heavy Ion Fusion

The process of longitudinal compression of a drifting heavy ion pulse to be used as an ICF driver is examined with the aid of particle simulation. Space charge forces play a vital role in halting compression before the final focus lens system is reached. This must take place with minimal growth of transverse emittance and momentum spread. Of particular concern are the distortion of longitudinal phase space by the rounded transverse profile of the longitudinal self-electric field. For application as an ICF reactor driver, a heavy-ion beam pulse must be longitudinally compressed by 1 to 2 orders of magnitude to achieve the peak power required to ignite a target. This process, among others, will be tested in a facility known as the ''High-Temperature Experiment'' in heavy-ion fusion. Beam compression is a critical element of an accelerator for heavy-ion fusion; it occurs primarily after the main phase of acceleration and before final focus onto target. Here we examine the compression of a drifting heavy-ion pulse with the aid of particle simulations. We describe initial theoretical results for an in-principle solution to this problem. Further refinements including integration into a complete driver system are necessary before the least costly solution can bemore » chosen.« less

Production of theK0K±π∓system inπ−pandK−pinteractions at 50, 100, and 175 GeV/c

The reaction ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{K}_{S}^{0}{K}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}}X$ has been studied at 50, 100, and 175 GeV/c. The observed $\mathrm{KK}\ensuremath{\pi}$ effective-mass spectrum is well described by a model assuming longitudinal phase space and two-body resonances. Production of resonances in $K\ensuremath{\pi}$ and $K\stackrel{-}{K}$ systems account for over 70% of the cross section. Estimated cross sections for $D(1285)$ and $E(1420)$ at 100 GeV/c are ${\ensuremath{\sigma}}_{D}B(D\ensuremath{\rightarrow}{K}^{0}{K}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}})<0.1$ \ensuremath{\mu}b and ${\ensuremath{\sigma}}_{E}B(E\ensuremath{\rightarrow}{K}^{0}{K}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}})=0.3\ifmmode\pm\else\textpm\fi{}0.2 $ \ensuremath{\mu}b. Results for the reaction ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{K}_{S}^{0}{K}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}}X$ at 100 GeV/c are also presented.

Bunch Lengthening in SOR

Bunch lengthening in SOR, a 400 MeV electron storage ring dedicated for synchrotron radiation experiments, was found to be induced by a longitudinal coupled bunch instability. The bunch length which increases as a 1/5.8 power of the beam current, can be explained by the balance between the growth of the instability and Landau damping due to the spread of synchrotron frequency, and by introducing a weak frequency dependence of coupling impedance. In connection with this phenomenon, slow fluctuation of synchrotron radiation was found to come from a detailed unbalance of the equilibrium electron distribution on the longitudinal phase space. Touschek life time of the expanded beam and Landau cavity to suppress the instability are described.

Electron Beam Dynamics in the CERN PS

The 28 GeV proton synchrotron (PS) forms part of the chain of LEP injectors with the rôle to accelerate positrons and electrons from 0.6 GeV, the operating energy of the Electron/Positron Accumulator (EPA), to 3.5 GeV, the positron/electron injection energy of CERN's 400 GeV proton synchrotron (SPS) which then accelerates the particles to 20 GeV. The PS used as an electron synchrotron has to supply the SPS with 8 bunches at an intensity of Nb = 8 × 109 particles per bunch. Bunch length and energy spread must be chosen carefully to avoid transverse and longitudinal single-bunch instabilities (turbulence) associated with high peak currents in the SPS. Analysis of the beam dynamics in the combined function lattice of the PS shows that this requirement can be fulfilled if the damning-partition numbers are changed. A Robinson Wiggler is proposed for this purpose and a new additional RF system is needed to produce the required bunch dimensions in longitudinal phase space.

A New Method for Longitudinal Emittance Measurements

A procedure for the measurement of beam parameters in the longitudinal phase space has been developed and tested at the Unilac. Approximating the particle distribution in the ?W-, ??-plane by ellipses the method will be practicable at all rf-accelerators if bunch width can be measured. Taking advantage of the broadband capacitive pick-up system of the Uinilac two different algorithms can be used for the evaluation of the relevant ellipse parameters. One algorithm is based on the measurement of the bunch width at different positions along the accelerator as a function of the drift length. The other one uses an rf-resonator operated at + 90° or - 90° stable phase with different amplitudes to vary the energy spread and therefore the bunch width at one pick-up. The Daper describes both methods and gives some examples from measurements at the Unilac.

Transverse Mode Coupling in a Bunched Beam

Since the fast transverse instability was observed in PETRA and, more recently, in PEP, this instability has become the problem of great importance for the design of large storage rings. The reason is that this instability imposes the serious limitation on a stored current; as soon as the current exceeds the threshold, the bunch distribution begins to blow up vertically or horizontally faster than the synchrotron-oscillation, and beam particles are lost. Short range fields created by the beam in rf cavities are considered to play an important role. The fast instability has been explained in terms of mode-coupling in the longitudinal phase space or "head-tail turbulence" by many authors. The purpose of this paper is to derive a formalism of the mode-coupling theory for a Gaussian bunch, starting from Sacherer's integral equation. The problem is reduced to solving the determinant equation for eigenfrequencies of coherent oscillations. Eigenfunctions are expressed as superposition of the linearly independent functions where higher radial modes and azimuthal modes are combined and rearranged into "hybrid modes". The theory is applied to explanation of the fast instability observed in PEP and to a preliminary estimate of the threshold current in the TRISTAN electron-positron storage ring. The transverse broad-band impedances of rf cavities in PEP and TRISTAN are calculated with the program code TBCI and characterized by a single low-Q resonator impedance. A satisfactory agreement with PEP experimental result is obtained.

Effect of Synchrotron Radiation in the Proposed 4-GeV Argonne Microtron

Synchrotron radiation in the sector magnets of the 4 GeV microtron designed at the Argonne National Laboratory produces a small but noticeable distortion of the closed orbits of the system and a very significant growth of the horizontal and longitudinal phase space emittances. Because of the small apertures in the three 25 meter linacs, it is important that the expected growth of the beam be calculated as accurately as possible. The dynamical problem has been solved using a computer program which follows the motions of individual electrons in the four dimensional horizontal and longitudinal phase space as they are accelerated in the system. In this paper the authors call attention to the fact that there are 3 long 28 m linac sections separated by sector magnets from 3 dispersion sections where the orbits for different energies are separated. The interaction of the linac rf systems with the synchrotron energy loss in the sector magnets produces different orbit effects in the downstream and upstream linac sector magnets. The average synchrotron radiation energy loss per sector magnet is given.

Longitudinal Phase Space Matching between Microtrons at 185 MeV

Electrons are accelerated to 185 MeV by a microtron. Then, they are injected into another microtron to boost the net energy up to a few GeV. Between the two microtrons both longitudinal and transverse phase space matching are required. In this paper, we consider a longitudinal phase ellipse matching which utilizes triple left-right-left sector dipoles to induce a negative phase angle shear. This is accomplished because a high energy particle travels a shorter distance through the dipole system than a low energy particle.

Beam Stacking Experiments at TARN

TARN is a low energy, around ten MeV/nucleon, ion storage ring aimed at beam accumulation in both the longitudinal and transverse phase spaces from the injector cyclotron. Up to now, proton, H/sub 2//sup +/, ..cap alpha.. and /sup 3/He/sup +/ beams have been stored and the close agreements are shown between the theoretical and experimental results on the beam dynamics. Twenty turn beams are injected in the betatron phase space area of 87 ..pi..mm X mrad by the multiturn injection method and 15 pulses are RF stacked in the momentum space ..delta..p/p of 2.2%. The overall stacking number is then attained at around 300 turns. RF stacking is performed with the repetition rate of 30 Hz and it requires about 0.5 seconds to fill the whole phase spaces with the beam. The e-folding life time of 7 MeV protons is 400 s at the vacuum pressure of 1 X 10/sup -10/ Torr, whereas that of /sup 3/He/sup +/ of the /sup 4/He gas target is 60 ms at 1 x 10/sup -8/ Torr. Collision strengths of charge exchange atomic reactions have been measured.

Equilibrium Bunch Length of Beam Current in Electron Storage Rings

A simple formalism for bunch lengthening in electron storage rings is given as an equilibrium state of the electron distribution in the longitudinal phase space, which is determined by the balance of quantum excitation, radiation damping, longitudinal coherent instability and Landau damping of the instability. The parameter dependence of the bunch lengthening is compared with other formulas. A numerical application of the new formula is given for several electron storage rings.

Comparison of 147 GeV/c π− p low transverse momentum hadron production with deep-inelastic leptoproduction

Distributions with respect toz andzR for the fastest and second fastest particles produced in both beam and target hemispheres from 147 GeV/c π− interactions are compared with each other and with the distributions for the fastest and second fastest particles from deepinelastic leptoproduction and Field-Feynman curves. The distributions and curves for the fastest particles are very similar, with the exception of the identified protons. Those for the second fastest are in agreement. Distributions with respect toz′R for the first through fourth fastest particles (excepting the protons) are all similar, suggesting that the shape of the distributions may be determined by the available longitudinal phase space.

Jet-like properties of multiparticle systems produced in K +p interactions at 70 GeV/ c

We present results on the jet-like properties of multiparticle systems produced in K +p interactions at 70 GeV/ c. The data analysed in terms of several variables commonly used to study the jet structure of an event. An extensive comparison is made with jets found in electron-positron annihilations and in deep inelastic νN interactions at comparable energy. Many similarities are found between low- p T jets in this experiment and jets observed in leptonic interactions. Our data are very well reproduced by the Field-Feynman quark fragmentation parametrisation but equally well by a longitudinal phase space model, suggesting that these similarities do not prove or disprove the universal character of the jet fragmentation.

Study of hadronic events inpp collisions at $$\sqrt s = 62GeV$$ and comparison with hadronic events ine + e ? collisions

We present an analysis of minimum bias events from proton-proton collisions at\(\sqrt s = 7GeV\) in the CERN ISR. We remove the effects of both the leading protons and compare theB=0 mesonic residue of the events to the hadronic events of similar energy produced ine+e− collisions. This comparison is presented in terms of the standard jet-type analyses involving quantities such as sphericity and aplanarity. We find significant differences between these data and the data frome+e− annihilations. The data of this experiment are consistent with the predictions of a longitudinal phase space model.

Calculations of Capture Efficiency of the Debunched Stack in ISABELLE

A computer program which simulates particle behavior in the longitudinal phase space has been developed to investigate the rebunching process and capture efficiency of the debunched stack in ISABELLE. A simple expression for a capture efficiency for an arbitrary initial distribution has been derived and used to estimate capture efficiencies for several assumed distributions.

On recent evidence for higher-twist effects in semi-inclusive deep-inelastic neutrino scattering

We discuss recent experimental evidence for higher-twist contributions in ν N → μ −h + X . We show that the observed effects are equally well reproduced by a longitudinal phase space model, with no free parameters. With an antineutrino beam instead the corresponding effect predicted by the LPS model is found to be opposite to that expected from the high-twist calculation, and thus a cleaner test of the theory is possible.