r - Proceedings of CERNconference on High Energy Accelerators and Instrumentation, p. 366. Also private cOrmlUnications

Proc. of Sea Island Conf. NAS-NRC 656, 234

Blosser, Gordon, and Arnette, manuscript in preparation. t,) be a possibly likely choice as an injection device with possible. 1 1

f FF<GSCSCla re evance or A type synchrotrons. Specific factors ---------------------------------------------------------------------2­ -~-------------4 R.S.l. 27, 106 -----------------~------------------------------------3­ r

'

'/"lp of r-f acceleration sch$mes can be considered for the

j

chrotron wi th possinle gains in efficiency in particular :

:

i tuations. QDjective evaluation of the injection capauility of cyclotrons is unfortunately handicapped at present by a sparsity of written reports on a number of pertinent aspects of cyclotron information and secondly, by the absence of experimental testing of a number jf design features indicated to be desirable. The present report is dn effort to partially alleviate the first of these handicaps by cOllecting and reviewing available information, principally from unpublished notes and private communications, relative to the performance to be anticipated from injector cyclotlons. It will be convenient to divide the discussion into three sections. Section II summari4es existing data on phase space characteristics of cyclotl~n sources. Sections III and IV view the cyclotron as a device for mapping source phase space char­ acteristics into phase space characteristics of the extracted beam

Prcc. of CERNConf. on High Energy Accelerators and Instrumentation, p. 205

Progress Report on Beam Extraction Studies for uak Ridge Cyclotrun Analogue II (available from authors on request) more appropriate for injector cyclotrons). I I. THE CYCLO lRvN SuURCE Let the rectangular coordinates x and y designate displacement at righL angles to the principal direction of motion of a beam of ------------------------------------------------------------------ 5 ­ particle, and Px and Py th, corresponding conjugate momenta. The phase space density of some small element of the beam is then the current (particles per unit time) in the element divided by the product of the spreads in energy, in x, in Px, in y, and in Py of the element. For injection purposes the spread in energy of the particles leaving the source is usually of small consequence (7)

If the spread in energy of the output beam from either a cyclotron or a linac were measured as a function of time with extremely fast equipment, an area of the form shown in the sketch at right would be obtained (with similar figures following in sequence spaced in time at intervals of 1 r-f period.) ----------.tThe energy spread S arise. from the source, the spread ~ from detailed features of ths iC­ celerating process. Due to matching difficulties between in­ jector and synchrotron a phase figure of the form shown nalst normally be considered from the point of view of the synchrotron as having a spread A+& unHonD in time. Since 6» & in the usual circumstance, the precise value of 8 is unimportant. --------~------------------------------------------------------and it is therefore adequate to consider the density in the x, Px' y, Py, ~ projection of the total phase space. Experimental determinations of this projection can be accomplished by allowing the beam to illuminate an aper~ure and measuring the current and angUlar divergence of the beam passing through the apert :are. The x, y spread of the beam is defined by the ape r~ure, the Px' Py spread by the angular divergence (for sMall angles e)i:: P./ P etc.) Note that for given spread in Px and Py the angular divergence in each dimension wl11 vary as p-l as the particles are accelerated, and the solid angle -2

The measurements were.ade by one of th~ authors (HGB) and results are bri.fly stated in Proc. of Sea Island Conf. HAS-NRC pub. 656 p. 203 -------_.-------------------------------------------------------------­ ion source of the type normally used in synchrotron injector preaccelerators. lbe results of the measurements give values from 21 to 58 amp/cm2 sterradian, the range of values corresponding to increasing voltage on the source extractor electrode up to approxi­.ately the limiting value for reliable operation. Assuming the maxi.ua can be achieved routinely, the value of 60 amp/cm2 'tenadian for a DC instrument at 250 Kv is set 88 a standard of comparison. As a eros. check we note that with the above value for the density, the full width full angle product for a 50 Mev linac with 1200 acceptance time and 5 ma average output during the pul.e i. inferred to be 1.4 milli-rad em "ich 18 in accord with no~al operating expectation for such a device. r-f ion Source 1. -~oeusing e lee trod Cu,' k,' rot t 2. •\ altull..'. <:'0 1< \

&R. J. Jones Rev. Sci. lnst.~, 532 output of a source of the type used by Smith to be reduced by a factor 0.18 when r-f extraction voltage is substituted for D.C., other factors being held constant. Applying this correction and the p-2 correction gives an emittance (D.C., 250 Kv equivalent) for the Smith source of 39 amps/cm 2 sterradian. ilie approximate equivalence of the result from the Smith data, and that from the Cockcroft Walton data is in accord with what would have been the most reasonable prior expectation, namely that the plasmas in the two sources are approximately equally effective as producers of collimated ions. At the risk of belaboring the obvious it is perhaps worthwhile to note that equivalence of source e~ittance in no way necessarily implies equivalence in emittance in the extracted beams of CockcroftWalton and cyclotron. As an example, measurements on the extracted -9­ beam of the Oak Ridge 86" cyclotron gave emitta,nce values a factor (8.).,' of 5 x 10~ lower than the Cockcroft Walton ~~l~es, after correction for energy and r-f duty ~~le (0.18), even though the cyclotron was equipped with a source of the same type used by Smith and with presumably comparable emittance. The result is indicative of the enormous diluti~n of filled phase space with unfilled which can occur

Heyn and Khoe Kong Tat, Proc. Sea Island Conf. NAS-NRC 956. 29

Allen, Chatterjee, Ernest and Yavin, R. S. I. ~, 813 . The operation, unfortunately, gives little detailed insight into the ex­ tent of possible distortions of the radial phase area in the transition through ~r =4/4, but at least it is indicated that the transition is not disastrous. For the three sector case, model magnet and computer studies of both field fall off

and isochronus (E3) (14.) designs have 13 Michigan State Univ. Master's thesis,(unpublished)

manuscript in preparation. been made at Michigan State. Results obtained show that for either type of field, with adequate accelerating voltage, source locations can be found such that the x, Px' y, Py' area from the source maps into the intermediate radius region of the cyclotron with negligible distortion. Field falloff designs would perhaps be preferred in an injector cyclotron since they result in acceptance of a somewhat larger axial phase area

we therefore consider fields of this type in further detail. Typical performance to be expected are illustrated in Figures 3-6, which are results from ref. 13. -12­ Fig. 3 shows the (B) employed in the studies, along with the corresponding radial and axial tunes, the tune data beginning at the radius of the first half turn for an assumed accelerating voltage of 280 Kv per turn. The strong lJ, in conj unc tion wi th a rel ati ve z. absence of axial non-linearities, implies at once that the axial motion will be free of appreciable distortion. The 1arge}J ~ in addi tion en­ hances both the axial phase space acceptance given by Eq. (1), and the axial space charge limit, the latter given in the absence of neutralization by the approximate expression where A is the full axial height of the beam, Eo the permittivity of tree space, GJ the particles rotational angular velocity. e the