Continuously displayed emittance measurementsJ. H. Billen Citation: Review of Scientific Instruments 46, 33 (1975); doi: 10.1063/1.1134040 View online: http://dx.doi.org/10.1063/1.1134040 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/46/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Flat panel display prototype using gated carbon nanotube field emitters Appl. Phys. Lett. 78, 1294 (2001); 10.1063/1.1351847 Emittance measurements at the ESRF Rev. Sci. Instrum. 66, 1974 (1995); 10.1063/1.1145774 Flat display based on the metal–insulator–metal emitter array J. Vac. Sci. Technol. B 11, 514 (1993); 10.1116/1.586853 Erratum: Continuously displayed emittance measurements [Rev. Sci. Instrum. 46, 33 (1975)] Rev. Sci. Instrum. 46, 1295 (1975); 10.1063/1.1134458 A Technique for Measuring Spectral Emittance Rev. Sci. Instrum. 43, 1027 (1972); 10.1063/1.1685825

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Continuously displayed emittance measurements J. H. Billen

University of Wisconsin. Madison. Wisconsin 53706-

(Received 16 September 1974; and in final form, 3 October 1974)

A device is described to display continuously on a CRT the emittance of an ion beam. The system uses electrostatic deflectors and small apertures to scan the beam's phase-space position and momentum coordinates. Measurements are reported of the emittance and brightness of the following beams produced by five different ion sources: H-, D-, He+, He-, C-, Di, 0-, NHi, A +, and Cu-. Also investigated was the emittance of an H- beam from a duoplasmatron direct-extraction source as a function of the radial displacement of the zwischen electrode, and the phase-space particle density distribution of an H- beam was measured.

INTRODUCTION

Besides beam intensity, one of the more important proper­ties of an ion source is the beam quality, as measured by emittance. A device to measure simply and quickly the emittance of an ion beam is therefore a valuable diagnostic tool for ion-source development and test work. In this article an emittance measuring system is described which provides a continuous display of the phase-space area oc­cupied by the particles along a coordinate transverse to the beam axis.

First, let us review the usefulness of the emittance and acceptance concepts and the appropriate units for com­paring the quality of different sources. Then we will con­sider the present device, and finally discuss emittance mea­surements for several different beams from five sources used on the University of Wisconsin EN tandem accelerator.

PHASE SPACE, EMITTANCE, ACCEPTANCE, BRIGHTNESS, AND LIOUVILLE'S THEOREM

In the Hamiltonian representation of a system of n particles there are 6n equations of motion and 6n initial conditions which determine the subsequent motion of the particles. The 6n initial conditions are the three position and three momentum coordinates of each of the system's n particles. In general, the behavior of the system can be specified by the trajectory of a single point in a 6n-dimen­sional phase space. For a typical ion beam such a general approach is impractical, since n is so large that the 6n initial conditions are always unknown. However, if the particles are noninteracting and if the motions associated with the three spatial dimensions are independent, then one can consider individual particle trajectories in each of the three two-dimensional phase planes. For this representation, Liouville's theorem declares1 that the phase space area occupied by a system of particles subject to a time-varying Hamiltonian remains constant in magnitude, though not in shape. For an ion beam in a beam transport system the theorem applies if aberrations of lenses and space charge effects are negligible. Thus, the emittance or phase-space

33 Rev. Sci. Instrum., Vol. 46, No.1, January 1975

area occupied by the beam is an essential parameter govern­ing the transmission of the beam through an accelerator or other transport system. Actual emittance plots often have elliptical contours,2 though other shapes are encountered depending on the details of the extraction or acceleration mechanism. Particles subject to a linear restoring force transverse to the beam direction will themselves execute elliptical trajectories in phase space.

"Acceptance" is the complement of emittance and is the phase-space area 'allowed by the geometry of the device (accelerator or beam transport system). To have 100% transmission, the emittance of a beam must be entirely within the acceptance of the device when both emittance and acceptance refer to the same point along the beam direction. Thus, lenses and steerers in a beam transport system serve to match the emittance of the beam with the acceptance of various components of the transport system.

For a beam travelling along the z axis, as shown in Fig. l(a), we note that the values of emittance in the two trans­verse phase planes (that is, along the x and y coordinates) are independent of each other. Particle coordinates in the x phase plane are defined by Fig. 1 (b). For typical ion beams, the divergence Ox of a particle is directly proportional to the

FIG. 1. The z axis is defined y

by the beam direction as shown in (a). A particle's phase-space coordinates in the x phase plane are illustrated in (b). For ion beams of interest P.«P. and p.~p.

x

r-----+Z

BEAM DIRECTION

(a)

~px x=o ____ xIL-_______

p_z ______ __

(b)

Copyright © 1975 by the American Institute of Physics 33

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34 J. H. Billen: Emittance measurements

P,-

a-

(0 ) FIG. 2. Phase-space ellipses in (a) the position-momentum and (b) the position-divergence phase planes. The areas of the two ellip­ses differ by a factor p,.

-----r---+-~---x

a

(b)

transverse momentum px, and the total momentum is ap­proximately equal to the z component of momentum pZ' For a beam whose energy does not change, Liouville's theorem applies in the position-divergence (x,Ox) space just as it does in the position-momentum (x,Px) phase space. As a result, we conveniently express emittance and accep­tance with dimensions of position-divergence (e.g., mm­mrad). In order to compare emittance values for beams of different energies, one must correct for the fact that a particle's divergence is a function of pz,

(1)

Consider the e11iptical phase-space diagram in Fig. 2(a). The area of the e11ipse is 7rPla and is a conserved quantity even as the beam energy changes. Figure 2(b) shows the same phase-space ellipse in the (x,Ox) plane. The angle a is related to h through Eq. (1),

a= Pl/pz.

The area of this e11ipse is 7raa. Emittance for an elliptical

34

phase space area is defined as 1/7r times the area occupied by the particles in the (x,Ox) plane. According to this definition, emittance is not conserved as beam energy changes, but the product of emittance and beam momentum remains constant.

There are two methods in general use for constructing an invariant quantity from emittance so that beams of different energy may be compared. One makes use of the fact that, for nonrelativistic beams, particle momentum is propor­tional to the square root of the energy. Thus, we define a quantity ca11ed momentum normalized emittance2,

~= (A/7r) (E)'l, (2)

where A is the (assumed e11iptical) area occupied by the particles of the beam in the (x,Ox) plane, and E is the beam energy. If A is measured in mm-mrad and E in MeV the uni ts of ~ are mm· mrad . MeV ~ . For nonrela ti vis tic beams and tandem accelerators where the acceptance limitation is at the stripper, such a momentum normalized emittance is useful, since it is directly a measure of the relative com­patibility of beams of different mass and energy with a given device acceptance. A11 emittance values in this article are momentum normalized.

With the other approach, one multiplies the emittance by the energy-dependent factors in the relativistica11y cor­rect expression for particle momentum,

p=moc{Jy, (3)

where {3=v/c and 'Y= (1_{32)-l. Thus one defines another "normalized emittance",

(4)

Since {3 and'Y are dimensionless, the units of ~N are the same as the units of A. Normalized emittance is appropriate for beams of very high energy, since it is relativistically in­variant. However, unlike the momentum normalized emit­tance defined by Eq. (2), normalized emittance is not, for beams of different rest mass, a measure of relative com­patibility with a given acceptance. For example, if both a

SUPPRESSOR POSITION SCANNING DEFLECTOR PLATES

ION L ~ BEAMc:::::::>~l.

SLV In RING

t FARADAY CUP

CONSTANT FRACTION

AMPLITUDE DISCRIMINATOR

Rev. Sci. Instrum., Vol. 46, No.1, January 1975

I

-----~ • FIG. 3. Block diagram showing the entire emittance measuring system.

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35 J. H. Billen: Emittance measurements

hydrogen beam and an oxygen beam have the same normal­ized emittance [see Eq. (4)J, and were accelerated to the same kinetic energy, the oxygen beam would occupy a larger region of phase space than the hydrogen beam. For comparing the quality of beams of different rest mass, either the momentum normalized emittance or the product of normalized emittance and the square root of the ion rest mass is necessary. In the example above, the oxygen beam would occupy four times the phase space of the hydrogen beam.

For many purposes the "brightness" of an ion source is important. While brightness is essentially the beam in­tensity per unit (spatial) area per unit solid angle, there are several different definitions3 of "brightness" arising from different conventions for expressing emittance. To calculate "brightness" from beam current and emittance one must know the detailed beam geometry4 (i.e., the shape of the emittance areas in the two transverse phase planes). For an axially symmetric beam with elliptical phase-space contours, the "brightness" is

(5)

where I is the beam intensity and A is the phase-space area transverse to the beam direction. Typical units of "bright­ness" are J,lA·mm-2 ·mrad-2• In our work, we generally determine the phase-space area occupied by a core of the beam containing about 90% of the total beam current. For. this situation, we define "brightness" as

(6)

where it is understood that the phase space area A is that occupied by the 90% core of the beam.

CONTINUOUS DISPLAY EMITTANCE MEASURING SYSTEM

The emittance measuring system uses parallel-plate electrostatic deflectors and small apertures to scan position and momentum coordinates transverse to the beam direc­tion, in the manner earlier suggested by Marsicanin. fi A similar device, but for intense (20 mA) higher energy (50 MeV) pulsed beams, and which employs magnetic rather than electrostatic deflectors, has been described by Sluyters, Damm, and Otis.6 Figure 3 shows a schematic of the present

'ON SOURCE

-Vz

f 1

-I d

l +Vz

(a)

ib,L i -+ bz (20.3 em) j (2.5em) I

A B (b)

35

1.1 mm APERTURE

~ 0.35 mm SLIT

FIG. 4. Geometry of (a) position selection system and (b) momentum selection system. Trajectories of some transmitted particles are shown for the proper instantaneous voltages on the deflector plates.

system. The beam passes first between two electrostatic deflectors whose 60 Hz voltages are 1800 out of phase. For small deflections the only net effect is vertical translation of the beam. Hence, the small circular aperture at A will transmit only the beam portion which was initially off axis by an amount x=kVI, where VI is the instantaneous de­flector plate voltage [= V10 sin(w1t)] and k=ql(l+s)/ Ed. The geometric factors l, s, and d are displayed in Fig. 4. The ion energy and charge are E and q, respectively. The third electrostatic deflector, driven at a frequency W2 large compared to 60 Hz, plus the slit at B, pass only those par­ticles whose divergence (0: transferse momentum) coordi-

,- 1m -,

I FARADAY CUP 3

FIG. 5. Schematic of our ion-source test stand. For routine measurement of beam intensity and mass analysis we deflect the beam down the cur­rent line. The emittance device is shown oriented to scan the vertical phase plane. For each emittance measurement we measure the total beam current on Faraday cup 2. The maximum beam current reach­ing Faraday cup 3 is monitored con­tinuously by the CONFAD circuit.

POWER SUPPLIES

GAP LENS \... FARADAY CUP 4

TEST STAND

Rev. Sci. Instrum., Vol. 46, No.1, January 1975

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lOOK

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IA

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-=-A47 A48

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3

100 K

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ffi tIJ:K

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82K 20 K

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SWEEP VOLTAGE AMPLITUDE

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o o 0 0

o B6 o

o B8 o B,o

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-=-B Wafer

FIG. 6. Circuit diagram of the sweep voltage power supplies. The position scan voltage has the line frequency, 60 Hz. A Hewlett-Packard model 200-B signal generator connected to "Input From Oscillator" supplies the momentum scan signal. The deflector plates are connected to terminals 1--4, while the signals fed to the oscilloscope first pass through the lumped delay lines to compensate for a delay of the blanking signal in the preamplifier and constant fraction amplitude discriminator.

Co) CI)

~

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~ iD :::I

m §! • ;: :::I

~ :I CD

= s:

j :::I ;-

Co) CI)

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37 J. H. Billen: Emittance measurements

FIG. 7. Circuit diagram of the pre­amplifler and cons tan t fraction am­plitude discriminator (CONFAD). The voltage sensitive preamplifi.cr with a gain of 104 provi,\es a 10 V output for current inputs as low as 1 nA. The CON FAD circuit re­sponds properly only to negativc­going pulses, so for positive beams we switch in a signal inverter be­tween the preamp and the CO 0J FA!).

I % RESISTORS

nate is8x =!?'V2 , where V z= Vzo sin(wzt) and!?' =yl(l/2+b2)/

[Erl(l+bl+b z)]. Sec Fig. 4 for the geometric factors l, h, and b2 • All ions which pass through both apertures are col­lected by a suppressed Faraday cup.

A schematic of our ion source test stand is shown in Fig. 5. The magnet bends the beam by 12° in the horizontal plane. Though the emittance device is shown oriented to scan the vertical phase plane, most of the results discussed below are emittanccs in the horizontal phase plane. We fmd no sig­nificant differences between emittances in the two orthogo­nal phase planes. To keep aberrations small, we use a large diameter (8.3 em) einzel lens and gap lens immediately following the extraction region. The effect on emittance of any remaining lens aberrations ,He included in our measurements.

Beam transmission through the emittance device is neces­sarily low because of the small apertures. For a 1.1 mm aperture and 0.35 mm slit indicated in Fig. 5, transmission (ratio of maximal current at Faraday cup.) to total beam current at cup 2) is typically 0.02 to 0.2%. The response of the preamplifler at very low currents limits our emittance measurements to beams of intensity;:::: 100 nA (measured at cup 2).

The voltage signals used to select phase-space coordinates in the beam are fed to the horizontal and vertical deflectors of an oscilloscope. The abscissa becomes the position coordi­nate and the ordinate the momentum coordinate. The

I--- 9.4 mm ---1 FIG. 8. Sample photograph showing the emittance of a 30 keY H­beam from a direct extraction Duoplasmatron. The total rectangular area scanned by the emittance device was 81 mm' mrad, of which 42% is occupied by the intensifi.ed portion. The emittance correspond­ing to about 90% of the beam particles is 1.9 mm·mrad·MeV" The boundary of the intensifi.ed area corresponds to 10% of the beam's maximum phase space density.

Rev. Sci. Instrum., Vol. 46, No.1, January 1975

680pl 470pl

20K

500 IK

3K

~-O-F-FS-E-T----' NULL -12V

300K I 551'1

-12V

3M

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470pl

100 K

(10 TURN)

BLANKING AMPLITUDE

DISCRIMINATOR LEVEL

37

PREAMP OUTPUT

BLANKING OUTPUT

constant fraction amplitude discriminator (CONFAD) supplies pulses to blank the CRT trace when the beam current reaching the Faraday cup falls below a selected fraction of its maximal value. The resulting trace directly displays the phase-space area occupied by the particles in the beam as an intensified area with a picture repetition rate of 60 Hz. Circuit diagrams for the sweep voltage power supplies, preamplifier, and CONFAD are shown in Figs. 6 and 7. The delay networks, also shown in Fig. 6, compensate for the delay of the blanking signal in the preamplifier and constant fraction circuits. The continuous display on the CRT permits one to adjust source parameters, alignment, etc. for minimum emittance. For a quantitative evaluation of the emittance, and for a permanent record, one photo­graphs the CRT trace. The exposure must be long enough to fill in the intensified area. Figure 8 is such a photograph. With a polar planimeter we measure the relative fraction of the rectangular area occupied by the intensified area. Since known geometry of the device and the known sweep voltages determine the rectangular area absolutely, no cali­bration of the planimeter, camera, or oscilloscope is neces­sary. For most of our measurements we set the discriminator level of the CONF AD circuit to 10%. Then the intensified portion of the trace corresponds to all points in phase space with greater than 10% of the beam's maximum phase­space particle density. By making several measurements at different discriminator settings, one obtains the phase-space particle density distribution of the beam.

ACCEPTANCE OF THE EMITTANCE MEASURING DEVICE

Clearly the acceptance of the measuring system must be larger than the emittance of the source under measurement. We first consider the acceptance of the position scanner. Figure 4 shows three particle trajectories for the instan­taneous deflector plate voltage Vl on the position scanning plates. The divergence coordinate of each emerging particle

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38 J. H. Billen: Emittance measurements

(

'1Ioo---X,

38

FIG. 9. Acceptance of the position scanner for two different deflector plate voltages. Only particles within a

--------~t==:t::=~t::===~=::;:~=-------..... small range (1 mm) are transmitted for a given instan­taneous deflector voltage, as indicated by the shaded parallelograms. The dashed line parallelograms indicate that the transmitted particles emerge on the device axis

ACCEPTANCE LIMITS

II -2d It II I

II _, d - -ton 2L

II II II II 'y---+--_I

is preserved, but for each voltage V1 there is a certain limited range in the divergence coordinate Ox of the trans­mitted particles. Figure 9 shows the acceptance of the position selection system referenced to the 1.1 mm aperture at position A for two different voltages V1. The shaded parallelograms are the portions of the beam accepted for the specified deflector plate voltages. The dashed line parallelograms indicate that these portions of the beam emerge on the system axis, but with the divergence coordi­nate Ox of each particle unchanged.

DIVERGENCE

SCANNER

ACCEPTANCE

POSITION

SCANNER ACCEPTANCE

LIMITS

Rev. Sci. Instrum., Vol. 46, No.1, January 1975

x with their divergence coordinates preserved. For the present device 118% is about 40 mrad.

Since one cannot scan regions of phase space that lie outside the "acceptance limits," one must choose the device geometry to insure that the beam being measured lies within these limits. We built the present device into a standard 5 cm beam tube, and as a result the deflector plate separation d is rather small. For the geometry shown in Fig. 4, the instantaneous acceptance of the position scanner (either of the shaded parallelograms in Fig. 9) is 39.5 mm·mrad. We have found that an amplitude V10 of 150 V is sufficient for displaying the emittance of any of the beams

x

FIG. 10. Superposition of the posi­tion and divergence scanners' ac­ceptance at instantaneous deflector plate voltages V, and V2, respec­tively. Position scan selects the region x, off axis in the beam. Di­vergence scan selects the coordinate 8". The dimensions of the accepted region for a 1.1 mm aperture and a 0.35 mm slit are shown in the inset. The area of the parallelogram is about 0.9 mm-mrad.

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39 J. H. Billen: Emittance measurements

TABLE 1. Emittance and brightness for specified total beam current.

Total beam Emittance Brightness

Source Energy current (mm·mrad· (nA'mm-"

Beam (keV) (/LA) MeVt) mrad-a)

DE W 30 28. 1.9 42. D- 30 7.1 2.2 8.1 0- 30 2.1 1.6 4.3 NH.- 30 0.58 3.0 0.35

DDTN H- 30 16. 1.7 28. NH,- 30 0.44 0.85 3.3

He He+ 25.4 88. 10. 3.8 He- 25.7 1.5 13. 0.040

PIG(R) c- 30 1.9 4.5 0.50 C,- 30 1.5 2.5 1.2 0- 30 2.9 1.3 9.1 A+ 20 7.2 5.2 0.98 Cu- 20 6.0 6.1 0.59

PIG(A) He+ 21 200. 5.4 27.

measured to date. For V 1° = 150 V the position scanner's total acceptance is 1110 mm·mrad for a 30 keY beam. We feel that the optimum design would utilize shorter and more widely separated plates requiring the use of higher voltages to scan the same range in the position coordinate. Indeed, one is not restricted to the uniform deflecting fields of long parallel-plate capacitors for obtaining uniform de­flection. 7 From an engineering viewpoint, an entirely dif­ferent type electrode (e.g., transverse cylinders) may be advantageous.

The resolution of the divergence scanner is determined by the aperture diameter at A, the slit width at B, and the overall length from A to B (see Fig. 4). Figure 10 shows the superposition of the position scan acceptance and the di­vergence scan acceptance for instantaneous deflector plate voltages VI and V 2 , respectively. The area of the small shaded parallelogram (see inset), for a 1.1 mm aperture and a 0.35 mm slit, is about 0.9 mm-mrad. The divergence scan acceptance does not limit the measurement in the way that the position scan does. All of the phase space accepted by the position selector may be scanned by the divergence selector if the voltage amplitude V20 is large enough. We need only scan between the limits 6max and 6m in (which depend on the position deflector plate voltage VI).

TABLE II. Range of emittance for several measurements.

Number Beam of current Emittance

measure- range Range Average Source Beam ments (/LA) (mm·mrad·MeVt)

DE H ...... 26 2.0 -8.1 1.5-5.3 3.6 H-b 49 2.1 -28.0 1.8-4.4 2.8 O- S 0.24-2.1 2.4-3.6 2.7

He He- 3 0.82-1.5 13.1-14.4 13.5

PIG(R) c- 7 1.4 -1.9 4.4-7.7 5.8 Cu- 3 0.5<ki.0 4.6--6.9 5.9

PIG(A) He+ 25 134-200 4.2-7.7 5.5

• Vertical phase plane. b Horizontal phase plane.

Rev. Sci. Instrum., Vol. 46, No.1, January 1975

39

EMITTANCE MEASUREMENTS

We have measured the emittance and brightness of several beams from five different ion sources. The results for maximum beam current (though not necessarily best emittance) obtained during our emittance tests appear in Table I. We made many measurements of a few of the beams with wide variations in source parameters. The ranges of emittance observed for these beams are listed in Table II. The ion source designations are: DE, direct extrac­tion duoplasmatron8 ; DDTN, duodehcatron,8.9 a direct ex­traction duoplasmatron with a hollow cathode arc in argon gas in place of a filament; He, an rf discharge source8 with a cesium charge exchange; PIG(R), a radial extraction sputter Penning source10 ; and PIG(A), an axial extraction PIG source now under development. All the emittance values in Tables I and II correspond to the core of the beam containing approximately 90% of the total beam current. The "brightness" is that defined by Eg. (6).

In direct extraction duoplasmatron sources, negative ions are found in the peripheral region around a hot phsma coneY To extract a beam of negative ions, one moves the plasma cone off the axis of the anode aperture, exposing the aperture to a high density of negative ions. In our DE source,7 the zwischen or intermediate electrode moves with respect to a fixed filament and anode. We investigated the emittance of a 30 keY H- beam as a function of the radial displacement of the zwischen electrode. The results appear in Fig. 11. The error estimates include a 10% random error in determining the photograph areas, and ±2 mm·mrad (±0.1 mm-mrad-MeVl) due to the finite resolution of the measuring device. Since we generally cannot use more than few microamperes into our accelerator, we adjusted other source parameters to limit the H- output to less than 7 p.A. Optimum performance occurs with a radial displacement12

of about 0.7 mm. Radial displacements much less than 0.6 mm produce excessive electron current loading of the extraction electrode.

4.0

-jlJI

~ > .. ~ 3.0

."

~ X X x

I I I I E X

I 6 "i E I x I

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1.0

! ~ OJ X

X

X x

0.0 0.5 1.0 1.5 2.0 2.5 3.0

ZWISCHEN RADIAL DISPLACEMENT (mm)

FIG. 11. Emittance vs radial displacement of the zwischen electrode for a 30 keV H- beam from a Duoplasmatron direct extraction source. Measurements for the zwischen nearly on axis were prevented by large (> 10 rnA) electron currents loading the extraction electrode .• -emit­tance; x-H- current.

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40

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J. H. Billen: Emittance measurements

f

I I

I !

I I ! I

I I

20 40 60 80

PERCENT OF MAXIMUM PHASE SPACE DENSITY

We determined the phase-space distribution of particles for a 30 keY H- beam by making several emittance mea­surements with different discriminator settings on the CONFAD circuit. Figure 12 shows a phase-space density profile for a DE source H- beam of 12.5 J.l.A. The abscissa is the percent of maximum phase-space density represented by the boundary of the enclosed phase-space area (see Fig. 8). The phase-space area enclosed within the boundary is plotted along the ordinate. The smaller error bars in Fig. 12 reflect a more accurate method for measuring the deflector plate voltages than that used for the data in Fig. 11. As regions of low phase-space density are excluded from the measurement, the emittance decreases rapidly at first, then more slowly as regions with greater than 50% of maximum phase-space density are successively excluded.

Beam emittances we have measured are consistent with observed transmission through our EN tandem accelerator. Transmission of DE, DDTN, and PIG(R) beams is gen­erally very good (80%-90%), while 50% particle trans­mission is common for He- beams, especially for low termi­nal voltage. The net acceptance Qf our EN tandem for singly charged particles is about 19 mm-mrad-MeV! at a terminal voltage of 2 MV. This is cl,etermined chiefly by the overlap between the low-energy beam tube acceptance and the stripper canal acceptance. The present stripper canal is 670 mm long, with an i.d. of 9.5 mm. An EN tandem with the original stripper canal (770 mm long, 6.4 mm i.d.) has an acceptance of 11 mm·mrad·MeVt at 2 MV. Although the accelerator acceptance is larger than any of

Rev. Sci. Instrum., Vol. 46, No.1, January 1975

40

" I 30 I>

(f)

rn

40

(f) FIG. 12. Enclosed phase space area vs percent of ;; maximum phase-space density represented by the n enclosed area's boundary. The abscissa is essentially

2.0 rn the discriminator level setting on the constant fraction ?;; amplitude discriminator (CONFAD). Maximum phase­rn space density for this beam was ahout 0.4 I'A· mm-l . I> mrad-l.

I II

3 3

10 ~ c e

100

the beam emittances we have measured, the larger emittance beams require better phase-space matching of emittance and acceptance shapes for good transmission.

ACKNOWLEDGMENTS

I would like to thank Prof. H. T. Richards for his advice and encouragement. I am also grateful to M. F. Murray for his assistance with the electronic circuits, D. P. WiItzius for his expert help in assembling the apparatus, and G. E. Uhing for his help during the early stages of development.

*Work supported in part by the U. S. Atomic Energy Commission. lA very general and elegant treatment of the Liouville theorem and

phase-space conservation can be found in A. J. Lichtenberg, Phase SPace Dynamics of Particles (Wiley, New York, 1969).

2A. P. Banford, The Transport of Charged Particle Beams (Spon, London, 1966).

3W. Walch~.r, in Proceedings 2nd International Conference on Ion Sources (Osterreichische Studiengesellschaft fiir Atomenergie Ges. m. b. R., Vienna, 1972), p. 111.

4F. Prevot and R. Becherer, Ref. 3, p. 146. DB. S. Marsicanin, Nucl. Instrum. Methods 75, 106 (1969). 6Th. J. M. Sluyters, R. Damm, and A. Otis, IEEE Trans. Nucl. Sci.

NS-14, No.3, 1143 (1967). 'W. Raeberli, Rev. Sci. Instrum. 44, 342 (1973). SR. T. Richards, Proceedings Symposium on Ion Sources, Brookhaven

National Laboratory Report BNL 50310, 1971, p. 295. 9G. M. Klody and R. T. Richards, Bull. Am. Phys. Soc. 17, 510

(1972); R. T. Richards and G. M. Klody, Ref. 3, p. 804. lOR. V. Smith, Jr. and R. T. Richards, Bull. Am. Phys. Soc. 18, 617

(1973). "G. P. Lawrence, R. K. Beauchamp, and J. L. McKibben, Nucl.

Instrum Methods 32, 357 (1965). 12See Ref. 10, Fig. 1, for duoplasmatron geometry.

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