A large solid angle, high stopping power Bragg curve spectrometer for coincidence measurements

512

Nuclear Instruments and Methods in Physics Research A306 (1991) 512-523 North-Holland

A large solid angle, high stopping power Bragg curve spectrometer for coincidence measurements A.D. Frawley, L.H. Wright, R.C. Kline, E.P. Gavathas and L.C. Dennis Physics Department, Florida State University Tallahassee, FL 32306, USA

Received 10 January 1991 A large acceptance, high stopping power, Bragg curve spectrometer has been developed for use in coincidence experiments with heavy ions . The electron collection fields are radial and position information is obtained from a resistive anode. The detector is 60 cm deep and operates at pressures of up to 2.5 atm of P-10 gas. It is mated to a scattering chamber which allows it to be moved out of plane during coincidence measurements. The detector design was aided by the results of computer simulations of the electron collection process in the detector, and of the signal processing in the electronics. The signals from the Bragg curve spectrometer are recorded in a waveform digitizer and the Bragg peak height, range, position and pileup rejection information are determined from software analysis of the recorded signals . Factors limiting the performance of the detector are discussed, and results obtained with the detector are presented.

1. Introduction Bragg curve spectrometers are gaseous ionization chambers in which electrons are collected along the direction of the detected particle, rather than perpendicular to that direction as in a conventional ionization chamber. The time dependence of the charge collected at the anode provides information about the energy, Z, range and, for lighter ions, the mass . Although Bragg curve spectrometers have no particular performance advantages over carefully optimized conventional ionization chambers, they are more flexible and their geometry is more suitable for the construction of compact detectors with very large acceptances . Since the first appearance [1] of Bragg curve spectrometers about 8 years ago, several large detectors of this type have been described [2-4] in the literature . Of these, the largest [2,3] use approximately radial electron collection fields so that electrons are collected along the direction of the incident particle over the entire acceptance of the detector. In some cases [4,5] thin multiwire proportional chambers have been used in front of Bragg curve spectrometers to provide timing and position information . In this article we describe a high stopping power, large acceptance, position-sensitive Bragg curve spectrometer (BCS) . The detector was developed for use in coincidence experiments with heavy ion beams at energies of about 10 MeV/u. It is mated to a scattering ' Research supported in part by the National Science Foundation .

chamber which allows it to be moved out of plane during coincidence measurements . The geometry of the detector provides a maximum usable solid angle of 77 msr, and the use of radial collection fields makes it feasible to segment the anode. In the present configuration, the acceptance is 35 msr and an unsegmented anode is used . One of the major design criteria for the detector was that it must have the capability of supporting a segmented anode, so that multiple hits from the same nuclear reaction could be separated. One consequence of this is that the electrons from a given charged particle must be collected to a point on the anode, and this in turn requires radial collection fields. Another consequence is that the use of a multiwire proportional counter in front of the Bragg curve spectrometer to obtain position information is ruled out, since such a detector could not simultaneously provide position information for more than one incident particle . Instead, the position information is obtained by using a resistive anode. 2. Description of the detector 2.1 . General

A schematic diagram of the detector mated to its scattering chamber is presented in fig. 1 and various design parameters are summarized in table 1. The BCS is mounted on a hemispherical cap which is attached to the chamber with a sliding O-ring vacuum seal, so that it can be rotated around the beam axis . The cap con-

0168-9002/91/$03 .50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)

A .D . Frawley et al. / A Bragg curve spectrometer for coincidence measurements Rotating Vacuum Seal

51 3

tied to present the minimum possible cross section to

Target Ladder

the target .

Faraday Cup

The entrance window of the detector is 39 cm from

Solid State etector Mount

the target, and the active gas volume is 60 cm deep . The detector uses P-10 gas and is designed to operate at pressures of up to 2.5 aim, at which pressure it will stop 160 . The about 12 MeV/u light ions and 26 MeV/u window material is 7.6 ~tm thick aluminized Kapton . With

the present anode configuration,

acceptance is 17' by 6.75' .

- Anode

Frisch Grid

f Signal Feedthrough Plate -Gas Outlet Gas Inlet

Fig. 1 . Schematic diagram showing the Bragg curve spectrometer mated to its scattering chamber. The detector is mounted on one of four ports in a spherical cap. The cap can be rotated around the beam axis. By changing ports and rotating the spherical cap, all angles between a 3 ° and a 60' half-angle cone can be covered. The scattering chamber contains two movable solid state detector arms . Only one arm has been shown.

the detector

2.2 . Mechanical and electrostatic layout The field shaping surfaces of the detector are cylin-

drically symmetric about its center line, and are shaped

so as to produce electron collection fields which point radially away from the target . The entrance window, Frisch grid and anode each form part of a spherical surface centered on the target. The equipotential surfaces

inside the active volume are correctly terminated by a set of 14 additional field shaping electrodes, each of which also forms part of a spherical surface centered on

the target . The width and separation of the field shaping rings were chosen on the basis of electrostatic field

calculations to provide effective shielding of the active volume of the detector from the walls and support

tains four ports for mounting the detector. By moving

structure. The window is operated at a voltage of -10

within a 60' half-angle cone centered on the beam axis . The central 3 ° half-angle cone is always shaded by the

accuracy) which add up to a total resistance of 97 MS2. The window support is electrically isolated from the

the detector between the four ports and rotating it around the beam axis, it is possible to cover all angles

kV per atmosphere of P-10 gas. The field grading is provided by a chain of custom made resistors (0.25

Faraday cup. If desired, a larger angle range around the beam axis can be blocked by adding a collar to the

front plate of the detector by a 3.5 cm thick annular

Faraday cup. The scattering chamber contains two movable detector arms, each capable of supporting a cooled solid state detector telescope . Each arm is desigTable 1 Bragg curve spectrometer design parameters Active depth Gas Maximum operating pressure Aluminized Kapton window thickness Maximum stopped energy : He 160 Acceptance : maximum present anode Entrance window optical transmission Frisch grid/anode separation Operating voltages : window Frisch grid anode Window/Frisch grid electron drift time

G-10 stand-off, which also holds the o-rings which make the vacuum seal between the window and the chamber. The Frisch grid to anode separation is 0.75

cm . The Frisch grid is a stainless steel mesh having a wire diameter of 0.152 mm and a mesh size of 1.52 mm by 1 .52 mm . The anode, Frisch grid and field shaping rings are all supported from the front plate of the

60 cm P-10

2.5 atm 7 .6 Win 12MeV/u 26 MeV/u 18' cone 17 ° by 6.75 ° 77% 0.75 cm -10 kV/atm 0V 333 V/aim 11 .2 Rs

detector by a G-10 frame.

The anode is made of fiberglass with a thin layer of

carbon evaporated

onto the active area

to make it

resistive . The part of the anode which is not used for charge collection has copper evaporated onto it with

only a small nonconductive gap in between the copperand carbon-covered surfaces. This allows a uniform electric field to be maintained between the Frisch grid

and the anode. Each end of the resistive carbon layer

terminates in a copper electrode evaporated onto the fiberglass. The carbon layer acts as a resistive divider when charge is collected from both ends, providing a measure of position along the active anode strip. This

carbon covered strip is 33 .4 cm long and 13 .9 cm wide,

measured along the spherical surface. The curved field shaping electrodes, the collar for the Frisch grid, and the mold for the fiberglass anode

514

AD

Frawley et al / A Bragg curve spectrometer for coincidence measurements

were made by having sheets of aluminum spun to the correct curvatures and then cut into the appropriate shapes . To get the Frisch grid to hold the required curvature the following procedure was adopted : A flat stainless steel grid was forced to take the correct shape by clamping it between two spun aluminum pieces . While it was still clamped in this way, the edges of the grid were epoxied to the aluminum collar. When the clamp was removed, the grid was capable of taking the required shape without having to be stretched. The Frisch grid and anode were then assembled into a single unit, with their 0.75 cm separation, and the grid was pulled into the correct shape by tying it to the anode to nine places using thin nylon thread passed through small holes drilled in the anode. The entrance window aperture has a diameter of 12 .2 cm, so at 2.5 aim the force on the window is considerable. The 7.6 [,m thick aluminized Kapton window is stretched across a stainless steel grid of 0.127 mm thickness and 2.5 mm square mesh size, which in turn is stretched across an aluminum web machined to have the correct curvature. A photograph of the window support, with no Kapton window mounted, is presented in fig. 2. The vanes in the aluminum web are 1.27 cm

Fig. 2 .

Photograph

of the structure

deep and are cut so that they present the minimum cross section to the target. The cross sections vary from 2 .5 mm for the center horizontal vane to 0.5 mm for the outer horizontal vanes. The 1 .0 mm wide vertical vane provides stability against buckling . When the window is pressurized there are, of course, departures from the desired spherical curvature as the stainless steel mesh stretches under the load . These departures are at most about 1 .5 mm at 1 atm (the only pressure at which we can observe the window under load) and do not noticeably degrade the performance of the detector. The overall optical transmission through the entire window support is 77%, with the stainless steel mesh contributing 90% and the support web contributing 85%. The overall optical transmission to the present single-strip anode is also about 77% . 2.3. The detector gas Because CFa has about 2.7 rimes the stopping power of P-10, it was initially planned that this detector use CF, at 1 aim. However, it was found that although CF, gave reasonable spectra at pressures of 0.25 aim or less with window voltages of - 30 kV/atm, the signal size

which supports the 7 .6 Win Kapton window. The aluminum vanes are that the cross section presented to the target is a minimum.

1 .27

cm deep and are cut so

A.D . Frawley et al / A Bragg curve spectrometer for coincidence measurements

decreased with pressure by (depending on the particle range) roughly a factor of two between 0.25 and 1 .0 atm . Similar behavior was obtained with isobutane. When signal size is plotted vs pressure for these two gases, it is evident that not all of the electrons are being collected even at 0.25 atm. It was concluded that both CF, and isobutane were too electronegative for use in an ionization chamber as thick as this one. In the absence of any other high stopping power gases with suitable properties, it was necessary to use P-10 gas at pressures of up to 2.5 atm to obtain the required stopping power. Experience has shown that there is no appreciable deterioration of the detector gas over 24 h if the detector is kept under high vacuum for at least several days before it is used . Therefore our usual practice while taking data is to replace the detector gas every 24 h, leaving it isolated in between. 2.4 . Readout electronics

The simplest electronics scheme for reading out a Bragg curve spectrometer involves splitting the anode signal . One branch is fed to a long shaping time ampli-

515

fier, the pulse height from which is proportional to the energy . The other branch goes to a short shaping time amplifier and then to a pulse stretcher, which produces an output equal to its largest input voltage. This gives a measure of the Bragg peak height, which is characteristic of the Z of the detected ion. In principle, this scheme could be generalized to read out the resistive anode of the present detector. However this was found to be impractical because of the effects of noise from the resistive anode on the pulse stretcher following the fast amplifier. If the peak detector in the pulse stretcher is not to limit the particle identification threshold, it must have a response time considerably shorter than 200 ns . Any peak detector having the requisite short time response is subject to detecting noise fluctuations in the leading edge of the pulse, causing the pulse stretcher to underestimate the Bragg peak height . This problem can be overcome by raising the threshold of the peak detector until it is greater than the largest fluctuations due to noise; however in the present application this causes at least some of the alpha-particles to be lost . A very simple readout scheme has been adopted instead. Fig. 3 shows the electronics used to detect x3 Detectors FF1

AMP

TFA

PULSE STRETCHER 15ys L_J____________ CFD

GATED INTEGRATOR 15Ns

LINEAR FAN OUT

LINEAR FAN IN /OUT

t PO

hon

sum

CFD

slop LOGIC FAN OUT

gate

13~ s delay

GATE & DELAY GENERATOR

- valid converston

COINCIDENCE (RANGE) TAC

TOF TAC

PULSE STRETCHER 15ps

PULSE STRETCHER 15Ns

EICS-E

LeCROY 2262 WAVE FORM DIGITIZER stop

Beam Pulsing

start

Range

TOF

FF I

I FF2 1 FF3

ORTEC AD 811 ADC strobe

Fig. 3. Schematic diagram showing the electronics scheme used to read out the Bragg curve spectrometer in coincidence with those solid state detectors which are set up for time-of-flight measurements relative to the beam pulsing. Tennelec TIC 174 charge-lntegratmg preamplifiers (external to the gas volume) are used for the Bragg curve spectrometer . They have been modified to reduce the tail length to 100 ~Ls to improve the resolution at high count rates. The 100 ns amplifiers are Ortec 474 timing filter amplifiers with the differentiation and integration time constants set to 100 ns . The Plullps 740 linear fan-in/fan-out module is used to sum and split the linear signals . The 1 tLs amplifier is the Ortec 570 spectroscopy amplifier, which is do coupled. The LeCroy 2262 waveform digitizer has 10-bit resolution and samples the signal 316 times . The sampling rate is set to 21 MHz, to give a 15 ~ts window. Tennelec TC861 time-to-amplitude converters are used for the "RANGE TAC" and "TOF TAC" .

51 6

A. D. Frawley et al. / A Bragg curve spectrometer for coincidence measurements

coincidences between the BCS and three solid state detectors . The signals from the anode are processed in charge-integrating preamplifiers and then in fast linear amplifiers before being sampled 316 times in 15 ~ts and digitized by a LeCroy 2262 waveform digitizer, which has 10-bit resolution . The digitized pulses can then be analyzed in software to yield Bragg peak height, position and range, and can also be examined for evidence of pulse pileup . Since the waveform digitizer samples for only 15 Ws, and the detector produces pulses up to 11 .2 ps long for long range ions, the pileup rate for pulses from the Bragg curve spectrometer could not be made much lower. With the scheme shown in fig . 3, a raw count rate in the BCS of 10000 Hz leads to a rate after pileup rejection of about 7400 Hz. It was found that integrating the digitized waveform to determine the energy led to poor energy resolution, particularly at high count rates . This is caused by small variations in the baseline of the signal as recorded by the waveform digitizer . These variations are partly due to low frequency noise pickup and partly due to the fact that the Ortec 474 amplifier is ac coupled . Instead, the BCS energy is determined by processing the summed anode signal in a dc-coupled Ortec 570 spectroscopy amplifier (1 Ws shaping time) and then integrating it for 15 gs in a gated integrator . The gated integrator output and all other signals are recorded in an ORTEC AD811 octal ADC . Events are recorded only when the Bragg curve spectrometer produces a signal within 12 ws of a signal from the telescope, stopping the coincidence TAC. The long time window is necessary because the Bragg curve spectrometer can produce a signal up to 11 .2 ws after an ion enters the detector, if the ion stops near the entrance window . The long coincidence window leads to a high accidental coincidence probability when the Bragg curve spectrometer count rate is high. True coincidences can be identified using the coincidence TAC output, since for true coincidences the TAC measures the time required for the end of the ionization track to drift to the Frisch grid . Therefore, neglecting flight times, the size of the coincidence TAC output signal is determined by the range of the detected ion . For a given Z, a display of the coincidence TAC output versus energy shows the true coincidences falling on a well-defined locus, with all other events distributed randomly. The readout scheme shown in fig . 3 is simple and cheap, and works well in our application . The low cost and simplicity will be very important when a segmented anode is added to the detector. However there is one disadvantage which should be mentioned . Because the waveform digitizer generates 632 samples for each accepted event, the conversion time in the waveform digitizer and the data transfer time in the CAMAC crate limit the data rate to less than 100 Hz. Since the detector is used only for coincidence measurements this

is sufficient for our purposes . If there was a need to take data at much high rates, some other readout scheme would have to be used . A more complicated but otherwise satisfactory scheme could be designed using gated integrators for analog determination of the Bragg peak height and position, using a 200 ns wide gate for the Bragg peak height and a longer gate for the position . A good analog pulse pileup rejector would be required. At the typical event rate of 10-20/s, the detector system produces data at a rate of 1 .3 X 10 4 to 2 .6 X 10 4 bytes/s . These data are written to a Digi-Data Corporation Gigastore 5 .4 VHS cassette tape drive, which has a storage capacity of over 5 Gbytes and a writing speed of 250 Kbytes/s .

3. Factors affecting the detector performance Details of the detector design and of the electronics scheme for processing the signals have significant effects on the energy resolution, Bragg peak height resolution, position resolution, particle identification threshold and maximum count rate . These effects and the steps taken to optimize the detector performance are discussed in this section . Section 3 .1 contains an overview of the factors which affect the detector performance . The effects of electron drift and diffusion in the gas are discussed in section 3 .2, effects of the resistive anode characteristics are discussed in section 3 .3, effects of energy loss straggling near the Bragg peak are discussed in section 3 .4, and the effects of certain characteristics of the signal processing electronics are covered in section 3 .5 . 1 3.1 . Overview For heavy ions, the most important contribution to the energy resolution of a gaseous ionization chamber is usually made by variations in the energy loss in the entrance window [6] . These variations result from both collision and charge fluctuation energy loss straggling in the window material, and from nonuniformities in the window thickness . In the case of the present detector, not only is the window necessarily thick because of the high operating pressures, but the window is stretched across the support structure in such a way that the window thickness varies with position . Therefore the energy resolution of this detector is expected to be somewhat poorer than would be possible for a detector with a flat, relatively thin window. There are two major contributions to the Bragg peak height resolution. The first is energy loss straggling in the region of the Bragg peak, which leads to fluctuations in the ionization density produced by the stopping ion . This is discussed in section 3 .4 . The effect of this on the Bragg peak height resolution can be reduced by

A D. Frawley et al / A Bragg curve spectrometer for coincidence measurements using a larger time constant for the fast amplifier which processes the signal from the detector . However it will be seen in sections 3.2 and 3.3 that the choice of time constant for the amplifier is heavily constrained by the need to keep the particle identification threshold as low as possible . The second major contribution to the Bragg peak height resolution is from noise due to the resistive anode. This is discussed in detail in section 3.3 . The ultimate limitation on the position resolution is the noise from the resistive anode. Again, this will be discussed in detail in section 3 .3 . At high energies, the time duration of the signal from the anode is determined by the range of the detected ion and the drift velocities in the gas. Particle identification is lost when the range of the detected ion becomes very short, because the length of the pulse from the detector is then dominated by the effective integration time due to the time constant of the amplifier, diffusion of electrons in the gas, and the Frisch grid to anode drift time . Under these circumstances the shape of the Bragg curve is attenuated and the measured Bragg peak height becomes a fixed fraction of the energy, regardless of the ion Z. The geometry and operating parameters of the detector and electronics must be chosen carefully to make the particle identification threshold as low as possible. This is especially important for the present detector because the high operating pressure leads to short ranges for heavy ions . A detailed discussion of these factors is given in sections 3.2 and 3.3 . The maximum useful count rate for the detector is set by the effects of count rate on resolution, and by pulse pileup rates. At high rates, pileup of the preamplifier tails can cause the linear input ranges of the following electronics modules to be exceeded . Thus is discussed in section 3.5 . To achieve the highest possible count rates after pileup refection, the maximum pulse width from the detector should be made as small as possible. 3 2. Effects of electron drift velocity and diffusion The electron drift and diffusion properties [7,8] of the P-10 gas impose limitations on the performance of the detector. The drift velocity of electrons in a gas is determined uniquely by the reduced field E/p. Therefore the electron collection time is independent of gas pressure if the window and anode voltages are scaled with the pressure . This is not so for the electron cloud diffusion. In a uniform electric field, the standard deviation due to electron diffusion after the electrons have drifted a distance x under the influence of an electric field E is given by [7,8] _( D x l1/2 ' ° -l2UEl

51 7

where D is the diffusion coefficient and U is the electron mobility . The experimentally measurable quantity D/U has units of V and, like the drift velocity, is determined uniquely by the reduced electric field E/p . The measured values of D/U are, in general, different for diffusion in the longitudinal and transverse directions. When electron diffusion is calculated from a theory [7,8], the results are given in terms of the characteristic energy Ek , which has units of eV . The calculated values of Ek are a prediction of the measured quantity eD/U, where e is the electric charge . Existing theories are capable of predicting only the transverse diffusion. The expression for the diffusion width can be rearranged to yield °

_(2

D l1/2 x l1/2 UÉl lPl

which shows explicitly the inverse square root dependence of diffusion on pressure, for fixed E/p. Because the electron collection fields in this detector vary with radial distance from the target, the electron drift velocities and diffusion rates are not uniform. Therefore a computer code was written to simulate the effects on the shape of the Bragg curve of the changing drift and diffusion rates as the electrons drift to the Frisch grid and are collected on the anode. Ranges were taken from Northcliffe and Schilling [9]. Electron drift velocities were obtained for P-10 gas from Christophorou et al . [10] . Transverse diffusion coefficients were obtained from the calculated curve presented by Walenta [11] which, in the range of interest, is similar to the calculated curve of Mathieson and El Hakeem [7]. No longitudinal diffusion coefficients were found for P-10 m the literature . Drumm et al . [12,8] have given experimental diffusion coefficients for a mixture of argon with CH, (10%) and iso-C,H, o (2 .8%), and it was assumed that the longitudinal diffusion coefficients for that gas could be used for P-10, since the transverse diffusion coefficients are almost identical to the calculated values for P-10 [11] . The results of these simulations were used to choose the operating voltage for the entrance window, the Frisch grid to anode distance, and the time constants for the amplifiers which process the signals. Because there is a peak in the curve of electron drift velocity versus applied field for P-10, there is a ratio of window voltage to gas pressure which minimizes the overall electron drift time from the entrance window to the Frisch grid . The minimum drift time of 11 .2 [s occurs at a window voltage close to -10 kV/atm, and so this value was adopted. Transverse diffusion is not of great concern in the present unsegmented detector, since the active area of the anode is sufficiently larger than the detector acceptance (limited by a collimator in front of the window) so that no electrons miss the active part of the anode at

A . D. Frawley et al / A Bragg curve spectrometer for coincidence measurements

51 8

any operating pressure of interest. However longitudinal diffusion, by smoothing the Bragg curve, contributes to loss of particle identification at ion energies which are low enough so that the range of the ion is comparable to the diffusion length . Because the applied field has been chosen to minimize the collection time, there is no freedom to vary it to reduce the longitudinal diffusion. For a short range ion, the FWHM longitudinal diffusion width at the Frisch grid is estimated to be 0.65 cm and the transverse diffusion width to be 0.49 cm, at a pressure of 2.0 atm and a window voltage of -10 kV/atm . Curve A in fig. 4 shows the shape of the digitized waveform as it would be for a 140 MeV 160 ion at 2.0 atm if there was no smoothing in the detector or amplifier. Curve B shows the calculated effect of the longitudinal electron cloud diffusion on the shape of the signal . Because electrons induce charge on the anode throughout their drift from the Frisch grid to the anode, additional smoothing of the time dependence of the signal occurs due to the Frisch grid to anode drift time . Clearly it would be desirable to minimize the gap between the Frisch grid and the anode, and to maximize the electron drift velocity in the gap. However two other factors must be considered . Reducing the distance between the Frisch grid and the anode increases the capacitance between these two electrodes, degrading the signal-to-noise ratio (see section 3 .3). Also, the effectiveness of the Frisch grid shielding of the anode decreases as the separation decreases, and the electric field between them must be relatively high to avoid electron capture by the Frisch grid [131 . The choice of 0.75 cm for the Frisch grid to anode separation and 333 V/atm

m w

0

150 100 50 0

Fig. 4 . Estimated shape of the digitized Bragg curve spectrometer sum signal for 140 MeV 160 at a pressure of 2.0 atm. Curve A shows the expected signal shape if there was no smoothing in the detector or amplifier. Curve B shows the effect of smoothing by the longitudinal electron cloud diffusion, curve C shows the additional effect of the Frisch grid to anode drift time of 200 ns, and curve D shows the additional effect of shaping in the Ortec 474 amplifier, with 100 ns differentiation and integration time constants. Each sample represents a time interval of about 48 ns.

for the voltage difference was a compromise in which anode capacitance, Frisch grid shielding and electron drift time all were taken into account. These parameters lead to a transit time to the anode from the Frisch grid of about 200 ns . Curve C of fig. 4 shows the calculated effect of this on the shape of the signal . An amplifier shaping time which is too long will smooth the Bragg curve too much, raising the particle identification threshold. Our simulations show that a reasonable value of the differentiation and integration time constant for the ORTEC 474 fast amplifier is 100 ns. For shaping times larger than this the particle identification threshold is judged to be too high . With shaping times of 100 ns, the calculated effect of the amplifier on the signal shape obtained for 140 MeV 16 0 is shown by curve D in fig. 4. 3.3 Effects of resistive anode characteristics Resistive anodes such as the one used here are inherently noisy. Because most of the noise generated by the resistive anode is canceled when the outputs from the two ends are summed to determine the energy and Bragg peak height, the most important effects of this noise are on the position resolution . A model which provides estimates of the limitations imposed by anode noise on the resolution of a detector such as this one has been described by Radeka [141 . The anode and Frisch grid form an RC transmission line which has a signal propagation time determined by TD

o

RDC D n

where RD is the total resistance along the length of the anode strip and CD is the total capacitance of the anode strip. To avoid nonlinearity due to different rates of charge collection at the ends of the anode, the amplifier shaping time should satisfy TF > TD/2 .

If it is assumed that the only important contribution to the position resolution is due to thermal noise in the resistance of the anode, the FWHM position resolution is given by [141 1/2 AL _ .316 kT aF2TF) L Qs (RD where AL is the uncertainty in the position due to anode noise, L is the length of the anode, Qs is the charge collected, k is the Boltzmann constant, and the product a F2 TF is defined by aF2TF=

f[ W(t)1 2 dt,

where W(t) is the weighting function of the amplifier and any other signal shaping electronics following the preamplifier .

A .D . Frawley et al / A Bragg curve spectrometer for coincidence measurements

The relative energy (or Bragg peak) resolution is given by AE

)1/2 0 .957 4 (kTC T aF' , QS D D TF

where the quantity "FI

aFi/TF

= f [W'(t)12 di,

is defined by (5)

where W'(t) is the differential of W(t) with respect to time. Note that the filter time constants may be different for the energy, Bragg peak and position determinations. The weighting function W(t) represents the response of the shaping network to a voltage step from the preamplifier (equivalent to a charge spike into the preamplifier) which occurred t seconds earlier [15] . It is normalized to unity at its maximum value. If the shaping is done by a single amplifier, the weighting function is dust the output pulse shape from the amplifier due to a voltage step from the preamplifier at time zero . The signal processing used here corresponds to an amplifier followed by a gated integrator . In that case the weighting function is obtained [15] by finding the overlapping area of the amplifier response and the gated integrator time window for all possible relative times between the start of the amplifier pulse and the opening of the integrator window, and normalizing the resulting function to unity at its peak . For simplicity, the amplifier response can be approximated by a piecewise fit of three straight lines, forming a trapezoid. This trapezoid can then be folded with the gated integrator window to obtain the approximate form of W(t) . The shaping network time constant TF used in eq . (1) was taken by Radeka [141 to be the base width of the weighting function . It is clear from eqs. (2) and (4) that, for a given TD , the effects of the anode noise can be reduced by reducing CD and increasing R D . However, as mentioned m section 3 .2, the separation between the Frisch grid and the anode was chosen to be 0 .75 cm as a compromise between anode capacitance and electron drift time across the gap. This results to a measured capacitance to ground for the anode strip of CD = 216 pF . With CD fixed, the position resolution is enhanced by choosing the anode resistance R D to yield the maximum acceptable time constant TD . However, as mentioned in section 3.2, the differentiation and integration times for the Ortec 474 fast amplifiers were chosen to be 100 ns to keep the smoothing of the Bragg curve acceptable . Given this, it is found from eq . (4) that for the noise contribution to the Bragg peak height resolution to be reasonable (1-2% for 16 0), TD should not be much

51 9

larger than 200 ns . Consequently, the anode resistance was set at 1 .12 kQ, corresponding to TD = 240 ns. With CD and R D specified, the contribution of anode noise to the energy resolution can be estimated from eq . (4), with Qs equal to the total charge deposited in the detector . Using a trapezoidal approximation to the (approximately Gaussian) measured Ortec 570 amplifier response and folding it into the 15 ws long gated integrator window, we obtain an estimate of 52 keV. This is negligible in comparison with other contributions to the energy resolution . The Bragg peak height is determined in software by integrating over a 200 ns wide region around the peak of the digitized Bragg curve. The weighting function was obtained for this case by fitting a trapezoid to the (CR-RC) measured response of the ORTEC 474 amplifier (with 100 ns shaping times) and folding it into a 200 ns wide window. To estimate the noise contribution to the Bragg peak height resolution, we set Qs equal to that portion of the charge which resides m a 200 ns wide region around the Bragg peak. Obviously, the value of Qs will depend very strongly on gas pressure and on Z in this case. From our simulations, for a 133 160 MeV ion Qs = 0.0811 pC (9.9% of the total charge detected) at a gas pressure of 1 .5 aim. Using this value, eq . (4) gives an estimate of the relative uncertainty in the Bragg peak height due to anode noise of 1 .2% at 1 .5 aim. This uncertainty will decrease with increasing Z of the detected ion because the ionization density in the region of the Bragg peak (and hence the value of Qs used in eq . (4)) will increase. The statistics of the energy loss rate in the region of the Bragg peak will also contribute substantially to the Bragg peak height resolution, and this will be discussed in section 3 .4. Recording the signals from the Bragg curve spectrometer for later analysis in software makes it possible to integrate only over the nonzero part of the digitized waveform. Thus the position resolution can be optimized for each event by minimizing the value of (aF2T ) 1/2 /Qs in eq . (2) . The weighting function for this case is obtained by folding a trapezoid approximating the measured response function of the Ortec 474 amplifier into a time window corresponding to the nonzero part of the waveform . For 133 MeV 160, for example, the position resolution estimated in this way is 0.35 ° at 1 .5 atm. 3 .4 . Effect of energy loss straggling on the Bragg peak height resolution

The energy loss straggling near the Bragg peak is dominated by charge fluctuation straggling . SchmidtBöcking and Hornung [16] have fitted a semiempirical formula to energy loss straggling data for Cl ions m P-10 . Kusterer et al . [171 give a simplified version of

520

A .D. Frawley et al. / A Bragg curve spectrometer for coincidence measurements

that formula which we can use to estimate the FWHM uncertainty in the energy loss over a specified interval : °E) A(AE) = KZ 1 1 2 (AE)' S(E, S(E) where Zp is the nuclear charge of the detected ion, K and y are parameters determined by Kusterer et al . from the work of Schmidt-Böcking and Hornung, and S(E) is the specific energy loss of the detected ion in the detector gas at energy E . For P-10 gas, y = 0 .53, K = 0 .026 MeV 0 47 . The contribution of charge fluctuation straggling to the Bragg peak height resolution was estimated using this formula and the simulation program referred to in section 3 .2 . After smoothing of the waveform by the electron cloud diffusion, the Frisch grid to anode gap and the fast amplifier, integrating over a 200 ns wide window around the Bragg peak leads to an estimated uncertainty of 2 .0% due to energy loss straggling for 133 MeV 160 at an operating pressure of 1 .5 atm . Combined with our estimated contribution of 1 .2% from resistive anode noise, we expect a Bragg peak height resolution of about 2 .3% at 1 .5 aim for 133 MeV 160 . 3 .5 . Effects of the signal processing electronics At high count rates, pileup of the tails of the preamplifier pulses can cause the linear input ranges of the following electronics modules to be exceeded, leading to signal distortion and loss of resolution. The TC 174 preamplifiers used here have been modified by reducing their feedback resistance from 1000 to 100 MSZ, reducing the length of the tail of the preamplifier pulse from 1 ms to 100 ws . This modification to the preamplifiers had the desirable side effect of reducing the amplitude of low-frequency microphonic noise caused by vibration of the Frisch grid relative to the anode. After the change, this noise dropped to 100 mV peak to peak at the preamplifier output . The contributions of electronic noise to the energy, Bragg peak height and position resolution were measured using a tail-pulser connected simultaneously to the test inputs of both preamplifiers on the BCS anode . The resolution measurements were made first with the preamplifiers connected to the BCS anode, and then with the preamplifiers disconnected from the anode . The measured FWHM noise contribution to the energy resolution was equivalent to about 730 keV in both cases, so evidently there is a large noise contribution to the energy resolution but it is not due to the resistive anode . The noise contribution from the homemade gated integrator was found to be responsible for a large fraction of this.

The measured noise contribution to the Bragg peak height resolution when disconnected from the anode was equivalent to 0 .7% for 133 MeV 16 0 at 1 .5 atm, and when connected to the anode it was equivalent to about 1 .2% . Thus the measured noise contribution from the resistive anode is very close to the prediction of section 3 .3, which was 1 .2% for 133 MeV 160 at 1 .5 aim, and the resistive anode noise dominates the overall electronic noise . The noise contribution to the position resolution was measured using a pulse equivalent in length to that from a 133 MeV 160 ion at 1 .5 aim . The measured noise was equivalent to about 0.5' when disconnected from the anode, and about 1 .2' when connected to the anode . Thus the noise contribution to the position resolution also seems to be dominated by noise from the resistive anode, but this is much larger than the 0 .35' predicted in section 3 .3 .

4. Results 4.1 . Comments This detector was designed to be used in experiments with lighter heavy ion beams at energies of about 10 MeV/u . All of the tests and all of the experimental 12C and 16 0 . There is work so far have used beams of no reason to expect that the detector would not perform 58 Ni) well for detection of much heavier ions (such as but the energy loss in the window would be relatively large for such heavy ions, even at high energies . For 58 example, a 290 MeV Ni ion would lose roughly 25 thick Kapton window . So to optiMeV in the 7 .6 [Lm mize the detector for heavier ions it would be necessary to use a thinner window and lower gas pressures. For best results the detector should be operated at a pressure just sufficient to stop the most penetrating ion of interest, to maximize the ranges . So far however, the detector has been operated at 1 .5 atm when alpha-particles are not of interest, and at higher pressures when they are . This is done mainly because it is convenient to operate the detector at a pressure above 1 atm . since the scattering chamber can then be opened without disturbing the detector gas handling system . This means, for example, that the detector can be moved from one port to another and be in use again within 60 minutes . Another advantage of higher pressures is that the higher ionization density provides a better signal-to-noise ratio . Fig. 5 shows a measured signal obtained for a 140 MeV 160 ion at an operating pressure of 2.0 atm . Also shown is the signal predicted by our simulation program for the same situation . The calculation does a good job of reproducing the shape of the observed signal .

521

A .D. Frawley et al. / A Bragg curve spectrometer for coincidence measurements 2000 250 2 200

a 1500

cr 150 ¢ W 0 H

ii

W Z Z

100

x

U_

50 ~I 25

I I I 50 75 100 SAMPLE NUMBER

I 125

1

Fig . 5 . Comparison of a measured digitized signal for 140 MeV 160

at 2.0 aim with the calculated signal . The calculated signal is curve D of fig. 4. It is normalized to the measured signal at the Bragg peak . Each sample represents a time interval of about 48 ns

4 .2 . Coincidence spectra

Figs . 6 through 8 show two-dimensional spectra from a measurement of coincidences between the Bragg curve spectrometer and a group of three surface barrier detectors, for reactions induced by 140 MeV 160 on a carbon-backed ThF4 target . The surface barrier detectors were set at laboratory angles of -30', -60' and -90 ° , and detected everything from alpha-particles to fission fragments. The Bragg curve spectrometer was in-plane, spanning the laboratory angle range 28 .8' to 45 .8 ° . The gas pressure was 2.0 aim for these measurements. Fig. 6 shows the length of the pulse as measured from the digitized waveform (somewhat loosely called the "range" here) plotted against the coincidence TAC output . For true coincidences, the coincidence TAC signal size is proportional to the drift time required for the first electrons to reach the anode of the BCS. Therefore, neglecting flight times, there is a unique correspondence between the coincidence TAC output and the range in the BCS, resulting in true coincidences appearing as the diagonal line in fig. 6. Accidental coincidences are spread uniformly over the coincidence TAC range. Approximately two thirds of the events in fig. 6 are true coincidences . Most of the accidental coincidences can be rejected by gating only on the events in the diagonal line in fig. 6 . The resulting spectrum of coincidence TAC output versus BCS energy is shown in fig. 7. Because the size of the coincidence TAC signal reflects the range of the ion in the BCS, true coincidences appear in distinct groups characterized by the Z of the ion detected in the BCS. Close inspection of fig. 7 shows that the number of accidental coincidences could be further reduced, if necessary, by gating closely on these Z groups . This is usually not necessary . Evidently the range is determined

U FW 0 Z

1000

500

0

0

500

1000

1500

RANGE (CHANNELS)

2000

Fig. 6. Coincidence data for 140 MeV i6 0 on a carbon-backed ThF4 target . The axis labeled "range" is actually the length of the BCS pulse as measured from the digitized waveform. The coincidence TAC output spans 15 lis. For true coincidences, the coincidence TAC output is uniquely determined by the range of the ion m the BCS (flight times are negligible) . Thus these events fall on a well-defined locus. Accidental coincidences are randomly distributed along the vertical axis . The intense vertical line is due to random coincidences involving elastically scattered ions detected in the BCS. The operating pressure was 2.0 aim.

400 800 1200 ENERGY (CHANNELS)

1600

Fig. 7. Coincidence data for 140 MeV 160 on a carbon-backed ThF4 target, after gating on the events in the true coincidence line in fig. 6. This shows total energy deposited in the BCS displayed against coincidence TAC output. Because the coincidence TAC output is uniquely determined by the range of the ion in the BCS, the true coincidences appear as distinct groups characterized by the Z of the ion detected in the BCS. The operating pressure was 2.0 aim .

52 2

A . D. Frawley et al. / A Bragg curve spectrometer for coincidence measurements

more accurately by the coincidence TAC than it is from the software analysis of the digitized waveform . The energy versus Bragg peak height spectrum corresponding to fig. 7 is shown to fig. 8. For oxygen, particle identification is seen to be maintained down to about 1 .75 MeV/u, below which the oxygen group merges with heavier ions . The threshold for particle identification for oxygen improves to 1 .5 MeV/u when the gas pressure is reduced to 1 .5 atm. The results of our simulations reproduce the observed particle identification thresholds very well . 4.3 . Energy, Bragg peak and position resolution

For 133 MeV 160 elastically scattered from a thin Au target, the FWHM energy resolution was found to be 1.14 MeV (or 0.86%). The same beam produced an energy spread of 433 keV in a silicon surface barrier detector. According to the results of section 3 .5, the energy resolution could be improved by reducing the noise in the signal processing electronics . However even if the noise contribution from the signal processing electronics could be eliminated completely, the energy resolution for 133 MeV 160 would still be about 870 keV (or 0.65%). It is expected that this is dominated by variations in the energy loss of the detected ions in the BCS window . The FWHM Bragg peak height resolution was measured to be 2.5% for 133 MeV 16 0 scattered from Au . From sections 3.3 and 3.4, the Bragg peak height resolution expected from resistive anode noise and energy loss

straggling is 2 .3%, in good agreement with the measured value. The dependence of energy and Bragg peak height resolution on count rate was checked with a 49 MeV 160 beam on a Au target . The energy resolution deteriorated by 25% at 14,000 Hz, while the Bragg peak height resolution worsened by 18% . At a raw count rate of 10 000 Hz, the rate after pileup rejection is 7 400 Hz . The position signal was calibrated and the resolution measured by setting the BCS in the horizontal plane and placing in front of it a mask containing a long vertical slit . The slit was 0.30' wide and could be positioned accurately at any angle. The position signal from the detector was found to be somewhat energy dependent and also nonlinear. The nonlinearity appears to be due to the fact that the width of the anode strip is comparable with the length . For 133 MeV 16 0 ions and 1 .5 atm operating pressure, the position resolution varies from 0.9' near the outside of the detector to 1.9' near the center . For 68 MeV 16 0 ions the position resolution varied from 1 .1 ° to 2 .2 °. These measured position resolution values are adequate for the experiments planned with the detector, but they are factors of 2.5 to 5 worse than would be expected based on eq . (2). The results of the pulser tests discussed in section 3.5 show that the noise is, in fact, mostly due to the BCS anode . The reasons for the discrepancy between the calculated and measured position resolutions is not yet understood.

5. Summary and conclusions

în w z z x Y

w a. c7

â mm

Fig. 8 Coincidence data for 140 MeV 16 0 on a carbon-backed ThF4 target, after gating on the true coincidence line m fig. 6. This is total energy deposited in the BCS displayed against Bragg peak height . The operating pressure was 2 0 aim.

A position-sensitive Bragg curve spectrometer with an acceptance of 17' by 6.75' has been developed for in-plane and out-of-plane coincidence measurements . The detector is 60 cm deep and stops up to 12 MeV/u 4He ions at the maximum operating pressure of 2.5 atm of P-10 gas . Computer simulations of the electron collection process in the detector and of the signal processing in the electronics were used during the design of the detector . The results of the simulations closely match the signal shapes observed from the detector . A waveform digitizer is used to record the signals from the detector, and the Bragg peak height, range, position and pulse-pileup rejection information are determined from software analysis of the recorded signals. For 133 MeV 16 0, the detector provides 0.86% energy resolution and 2.5% Bragg peak height resolution at an operating pressure of 1 .5 atm. The energy resolution deteriorates by 25% and the Bragg peak height resolution by 18% at a count rate of 14000 Hz for 49 MeV 16 0. The FWHM position resolution varies with position and improves with increasing ion energy and (slightly) with increasing gas pressure . At 1 .5 atm, it

A .D. Frawley et al / A Bragg curve spectrometer for coincidence measurements falls in the range 0.90 ° to 2.20 ° for 68 to 133 MeV 160 ions .

Coincidence spectra measured with the detector show

very good particle identification, and rejection of accidental coincidences and pulse-pileup events is effective.

The particle identification threshold is at about 1 .75 MeV/u for 160, at an operating pressure of 2.0 atm.

References [1] C.R . Gruhn et al ., Nucl . Instr. and Meth . 196 (1982) 33 . [2] R.J. MacDonald et al ., Nucl . Instr. and Meth . 219 (1984) 508. [3] C.D Westfall et al ., Nucl . Instr. and Meth A238 (1985) 347 [4] M.F . Vineyard et al ., Nucl . Instr. and Meth . A255 (1987) 507. [5] A. Moroni et al ., Nucl . Instr. and Meth . 225 (1984) 57 . [6] K . Kusterer et al ., Nucl . Instr. and Meth . 177 (1980) 485

523

[7] See for example : V. Palladino and B. Sadoulet, Nucl Instr. and Meth . 128 (1975) 323; G. Schultz and J. Gresser, Nucl. Instr. and Meth . 151

(1978) 413 ; E. Matlueson and N. El Hakeem, Nucl . Instr. and Meth. 159 (1979) 489. A review and compilation of measured and calculated drift velocities and diffusion coefficients is given by : A. Piesert and F. Sauli, CERN Report 84-08, 1984 . [9] L.C . Northcliffe and R.F . Schilling, Nucl . Data Tables A7

(1970) 233. [10] L C. Christophorou et al ., Nucl . Instr. and Meth . 163 (1979) 141 . [11] A.H . Walenta, IEEE Trans. Nucl Sci . NS-26 (1979) 73 .

[12] [13] [14] [15] [16]

H. Drumm et al ., DESY 80/38 (1980) . O. Buneman et al ., Can. J. Res. A27 (1949) 191 . V. Radeka, IEEE Trans. Nucl . Sci. NS-21 (1974) 51 . F.S . Goulding, Nucl . Instr. and Meth 100 (1984) 493. H. Schmidt-Bucking and H. Homung, Z. Phys . A286 (1978) 253. [17] K. Kusterer et al., Nucl . Instr. and Meth . 177 (1980) 485.