Miyahara, Y

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Particle Accelerators, 1990, Vol. 28, pp. 113-118Reprints available directly from the publisherPhotocopying permitted by license only© 1990 Gordon and Breach, Science Publishers, Inc.Printed in the United States of AmericaEXPERIMENTAL AND THEORETICAL STUDIES ON THE LONGITUDINAL MOTION OFTRAPPED IONS IN AN ELECTRON STORAGE RINGYOSHIKAZU MIYAHARASynchrotron Radiation LaboratoryUniversity of Tokyo3-2-1, Midori-cho, Tanashi, Tokyo 188, JapanAbstract Longitudinal motion of trapped ions in an electron sto-rage ring was studied by observing l' -ray intensity responding to apulsed voltage applied to a clearing electrode. In ~d~ition theore-tical analysis was mode on the motion under the ExB force due tothe electric field of electron beam and the magnetic field ofbending magnet particularly in the fringe field region.INTRODUCTIONIn electron storage rings residual gases are ionized by the collision ofelectron beam and additionally by the interaction with synchrotronradiation. The positively charged ions are trapped in circulating elec-tron beam and induce harmful effects such as tune shift, broadening ofelectron beam and decrease of beam lifetime. Thus it is desired toelimin,ate the trapped ions to a sufficiently small extent. This has beendone with a considerable success by RF knock oui; clearing electrode2 andpartial fill of beam bunchs in RF buckets~ In order to eliminate thetrapped ions sufficiently, it is useful to know the properties of trap-ped ions.So far longitudinal motion of trapped ions has slightly been under-stood. We have investigated this property experimentally in SOR-RING bythe method of clearing electrode~1Sand found that longitudinal averagevelocity of trapped ions is about 950 m/s. This is considerably fasterthan the thermal velocity 290 mls of CO gas. It has been known theoreti-6 -cally that the trapped ions are accelerated by the ExB force, where E is-the transverse electric field in the electron beam and B is the verticalbending field. Thus the faster exmerimental velocity is consistent withthis acceleration. We have made a further analysis of the ExB forcetaking into account the fringe field of bending magnet, and foundthat the trapped ions are reflected by the fringe field or transmitted[591]/113114/[592] Y. MIYAHARAthrough the bending field depending on the initial condition of trappedions.EXPERIMENTAL RESULTSWe have applied a dc voltage on a disk-shaped position monitor,being used as a clearing electrode in the present experiment, and obser-ved a-ray intensity at first with a ,-ray survey meter at a positiondownstream. The r-rays are emitted by the collision of electron beamwith residual gases and trapped ions as well as by the collision of out-going electrons with the vacuum chamber of the storage ring. When apulsed voltage was applied to the electrode, the Y-ray intensity isreduced substantially as shown in Fig.1. The reduction is caused by theelimination of trapped ions, and implies that the trapped ions travelvery fast longitudinally in the electron beam. When the voltage isturned off, the ~-ray intensity recovers to the former level quickly,which is due to a fast production of trapped ions. The reduction satu-rates above an applied voltage of 1 kV for vertical disk gap of 13 cm,which is approximately in accord with the estimated maximum electricfield of 100 V/cm in the electron beam.The -0 -ray intensity was monitored at several positions around thering. Figure 1 shows the dependence of o-ray reduction on the distancefrom the clearing electrode. The reduction decreases symmetrically forupstream and downstream. This implies that the trapped ions travel inthe same ways in both directions upstream and downstream.3rLf r_roYLt:;j ~'1 l'~a>-? 2~-~-_tS~3:LD,[lo 60 120t(sec)al,Or------------------,. .0.5belectrodeIII-----L:-""=--=-l=-7,4-m-------~FIGURE 1 Response of a-ray intensity to a pulsed voltage appliedto a clearing electrode. (a)Dependence of 0 -ray reduction on the distance s fromclearing electrode. (b)LONGITUDINAL MOTION OF TRAPPED IONS [593]/115Next in order to see the velocity of trapped ions we have applied asharp pulsed voltage with a rise and fall time less than 10 f1 s, andmonitored the a-ray intensity with a NaI synchilator. The photo-pulsesfrom the synchilator were accumulated in a multi-channel analyzer. Thepulsed voltage with a width of 80 ms was repeated every 400 ms, withwhich the anlyzer was triggered. Figure 2 shows the examples of theaccumulated photo-counts monitored at several positions against the timedelay from the trigger.700 '------'----'-_~--A.-.--'_ _'____'_---J900 r----r--r--,----r----,---r---,---,87200730m/s630m/s IVi 10 \ •• 0.s 0.?00 0 0\>-;\~~.kl'l..l:/./\~\.,..., ::ft'('l.(~Mj·tA.;"!'".;'\,'.'r ... soL=17.4 m6020 40t (ms)o500FIGURE 2 Fast response of -0 -ray intensity to a sharp pulsedvoltage (a), and half decay time t l(2 against the distance s (b).The half decay time t,/;2..of the photo-counts or o-ray intensity isplotted in Fig.2 against the distance. By the root mean square fit wefind that the velocity of trapped ions corresponding to the halfdecay time is 630 mls for upstream and 730 mls for downstream, which arethe same within experimental errors. Assuming a Gaussian distribution ofvelocities of trapped ions we can reproduce the decay curves of 0' -rayintensity at a given distance. This results in an average velocity about950 m/s.The trapped ions related to the present experiment is thought to beCO+ because the production rate and emission rate of a-rays, both ofwhich being proportinal to atomic number, are much larger for CO+ thanfor H2+. At the instance when CO molecule is ionized, the initial116/[594] Y. MIYAHARAvelocity of CO+ is thought to be the same as the thermal velocity of COgas because the reduction of T -ray intensi ty and velocity of trappedions are symmetric for upstream and downstream.THEORETICAL RESULTSAs mentioned before the trapped ions are accelerated by the ExBforce in the bending magnet. The drift velocity by the force is expres-sed as(1)wherewxis the oscillation frequency due to the electric field, We thecyclotron frequency due to the bending field and X o and V o are initialhorizontal position and longitudinal velocity of trapped ions. Since theions are produced by the collision of electron beam, the initial posi-tion of trapped ions is thought to distribute in the same way as theelectron beam. Then substituting numerical values for the parameters inEq.(l) we find the average drift velocity (vd> ~ 3000 miseIn Eq.(l), xowc is much larger than vo ' so that it is supposedthat at the entrance of bending magnet, half of the trapped ions arereflected by the bending field and the other half are transmittedthrough the bending field. But in realty the fringe field of bendingmagnet changes gradually, so that the reflection and transmission oftrapped ions are affected to some extent by the fringe field. We havemade a theoretical analysis of the motion of trapped ions in the fringe- 23 &rA><= 1.1- T- .t'(25 m. xoo- 0 m/s 2S.an~'(. 1.1 SIG>ia .00 6 S-.2 lT~ 0 1)(00-0 YC>=0 Yroa~b2.S t------<-------...............----------I20 70 80y(mm)130 20 70 y(mm)FIGURE 3 Simulation of the motion of trapped ion under the ExBforce. (a) and (b) represent the motion of a trapped ion with asmall and large initial position xo.LONGITUDINAL MOTION OF TRAPPED IONS [595]/117field. It was found that the ions are reflected under the followingconditionwhere wc(Bmax ) is the cyclotron frequency at the maximum bending field.Figure 3 shows examples of numerical simulation of the motion of trappedions in the free space and bending field including fringe field. Ionswith a small initial amplitude are transmitted through the bendingfield, while the ions with a larger initial amplitude are reflected by1,5 x0,150.21x0.64 0.9010x x'x0,710,50.43Yo=2.22 Xl06xo0,91x x 0 00,75x1000 2000 3000Yo(m/s)FIGURE 4 Map of reflection and transmission of trapped ions withrespect to the initial condition Xo and vo(=Yo).the fringe field, and the reflected ions are again reflected by thefringe field in the opposite site. Thus the fringe field works as apotential barriar for the longitudinal motion of trapped ions.Figure 4 shows the map of reflection and transmission with respectto the initial condition of X o and vo(=Yo).The boundary of the reflec-tion and transmission in the same figure is close to the condition (2).In the same figure the shaded region represents the initial condition oftrapped ions in the storage ring. Thus, almost all trapped ions producedin the free space are reflected by the fringe field, and consequentlysuch ions are bounded in the free space. On the other hand the trappedions produced in the bending magnettravelthrough the bending field andfree space, and therefore circulate around the ring. According to thesimulation the velocity in the free space is 1.7 times faster than thedrift velocity in the bending field. Taking into account the length of118/[596] Y. MIYAHARAbending field (8xO.86 m) and free space (8xl.81 m) we find an averagevelocity 4400 mls of trapped ions for the circulation. This is much.faster than the experimental velocity of 950 m/s. The reason of thisdifference is not known yet. The amounts of the bounded ions in thefree space and the circulating ions around the ring are proportional tothe production rate of ions in the free spaces and bending magnets,respectively,which are approximately proportional to the length of freespace and bending magnets. Therefore about 30 % of trapped ions areexpected to circulate around the ring. The circulating ions are relatedto the reduction of T -rays when the pulsed volateg is applied to theclearing electrode.It is known that the electric potential produced by the electronbeam is deeper in the region of larger vacuum chamber, and that the ionsproduced in such a region are bounded there. The present analysis indi-cates that even if the chamber size is almost the same all around thering, the trapped ions produced in the free space are bounded there.Accordingly it is necessary to install clearing electrode in all freespaces to eliminate the trapped ions sufficiently.In multipole wigglers and undulators the bending field variessinusoidary. The ions produced in weaker field regions of such insertiondevices are bounded there. The ratio of bounded ions in an undulatorwith a peak field of 0.4 T and period length of 6 cm, for instance, isabout 35 %. To eliminate them it may be necessary to install a stripline type of clea~ing electrode.REFERENCES1. Y.Miyahara, Jpn.J.Appl.Phys. 1Q 1544 (1987).2. T.Kasuga etal, Jpn.J.Appl.Phys. 24 1212 (1985).3. M.Q.Barton, Nucl.Instr.Methods, A 243 278 (1986).4. Y.Miyahara, J.Vac.Sci.Tech. A 2.. 2927 (1987).5. K.Watanabe etal, Jpn.J.Appl.Phys. ~ L1964 (1987).6. R.D.Kohaupt, Internal Bericht, DESY Hl-71/2(1971).7. Y.Miyahara etal, Nucl.Instr.Methods A 270 217 (1988).

Experimental And Theoretical Studies On The Longitudinal motion Of Trapped ions In An Electron Storage Ring

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