Absolute energy calibration of a low-energy accelerator by the time-of-flight technique

Nuclear Instruments and Methods 1n Physics Research A274 (1989) 419-424 North-Holland, Amsterdam

419

ABSOLUTE ENERGY CALIBRATION OF A LOW-ENERGY ACCELERATOR BY THE TIME-OF-FLIGHT TECHNIQUE K. NELDNER, H.W . BECKER, S. ENGSTLER, M. KÖSTER, C. ROLFS, U . SCHRÖDER, W.H . SCHULTE and H.P . TRAUTVETTER Institut für Kernphysik, Universität Münster, Münster, FR G

K. BRAND Dynamttron Tandem Laboratorium, Ruhr-Universität Bochum, Bochum, FRG

Received 2 June 1988 The absolute energy of the proton beam from the 100 kV accelerator in Bochum has been measured using electrostatic deflection plates and a microchannel-plate detector as start and stop devices in a time-of-flight setup, respectively . The measurements confirm the absolute energy determinations made by a calibrated resistor chain, within a mean deviation of ±26 eV . 1. Introduction The determination of the stellar rates of charged-particle-induced reactions requires the measurement of cross sections at energies far below the Coulomb barrier [1-3]. Due to the steep drop of the cross sections at sub-Coulomb energies (nearly exponentially), a precise knowledge of the absolute projectile energy E is often as important as the precision of the yield measurements . For example, in the D + D fusion reactions [4] an absolute uncertainty of 4E = ± 0.5 keV at E = 10 keV leads to an error in cross section of Da/a = ±40`90, while the same uncertainty at E = 70 keV causes only a small error (Qa/a= ±2%) . The absolute energy of an ion beam from an accelerator is most commonly determined by an analyzing magnet, which must be calibrated, e.g ., by using the energies of narrow resonances or of thresholds in nuclear reactions. Lists of recommended calibration energies are readily available [5-7] and many examples of such calibration procedures can be found in the literature (e.g . ref. [8]) . However, there are no absolutely known calibration energies for ion energies below 100 keV. Thus, the high voltage U (at which the energy of the projectiles with charge state q is E = qU) of the high-current 100 kV accelerator in Bochum [4] was determined from the settings of the 100 kV power supply (FUG, model HCN700M-100000 : ripple = ±2 .5 X 10 -5 at full load). In addition, the high voltage was measured via a precision resistor chain (resistance = 1 GO) in series with a * Supported in part by the Deutsche Forschungsgemeinschaft (Ro429/15-3). 0168-9002/89/$03 .50 © Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)

high-precision digital current meter. This unit was calibrated at the Physikalisch-Technische Bundesanstalt in Braunschweig with an accuracy of DU/U= ±5 X 10 -° . Both determinations of the high voltage were found to be in good agreement . In view of the above discussion, however, a direct and independent determination of the absolute ion beam energy appeared desirable. This paper reports such a determination of the energy of a proton beam using the time-of-flight (TOF) technique (e .g . ref. [9] and references therein) . Details of all aspects of the present work beyond those reported here can be found in ref. [10] . The speed v of a proton can be determined by measuring the time t that it takes to travel a measured distance l in free space. The kinetic energy E of the proton can then be deduced knowing its speed, its rest energy, Eo = 938279.6 keV [111, and the speed of light, c = 2.99792533 X 10 1° cm/s [12], using the familiar result of special relativity : C E=EO[( I-v2/ 2 ) -1/2-1 1 ) -1/2 _ 1] =EOI(1 _ 12/(t2c2) For example, at E = 50 keV, one finds 1/t = 0.30948 cm/ns. For the precision in a determination of E, one obtains AE/E= [(AEO1EO) 2 + (20c/c)2 + (2A1/1)2 1/2, +(20t/t)2 ~

where DEO/Eo(= ±2 .8 X 10 -6 , [111), Ac/c(= ± 2.4 X 10 -7 , [12]), 01/l, and t1 t/t are the fractional uncertain-

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K. Neldner et al. /Absolute energy calibration by TOF technique

166cm

233cm CHEVRON MCP

90° BENDING MAGNET

SLITS ELECTROSTATIC COLLI(025mn) QUADRUPOLE MATOR TRIPLET (05mmO) LENS

ELECTROSTATIC PLATES

COLLI- MCP-DETECTOR MATOR (MOVABLE (05mmO) OVER 16cm)

FARADAY CUP

Fig. 1 . Schematic diagram of the experimental setup at the 100 kV accelerator m Bochum [4]. The proton beam was deflected periodically by applying a square-wave voltage (+15 to -15 V) to the electrostatic plates . At the crossover time of the voltage, the protons leave the plates on the beam axis and are observed using the secondary electron emission of a carbon foil . This electron emission was detected with Chevron microchannel plates (MCP). ties in the rest energy, speed of light, flight path length, and flight time, respectively . The first two of these contributions to the desired overall precision of DE/E = ±10 -3 are negligible ; thus AE/E = 2[ (O1/1)

2

+ (

'~

t/t

)21

(2)

and the fractional uncertainties both in A1/l and Ot/t have to be smaller than about ±5 x 10 -4 . These requirements, together with the limited space available at the 100 kV accelerator in Bochum (i .e ., relatively short flight paths), dictated the experimental setup for the TOF technique (fig . 1), described below.

plates . Approximately at the zero crossover time of the applied voltage, the protons leave the plates on the beam axis, and are observed with the MCP detector (section 2.2). In this arrangement, the zero crossover time of the applied voltage provided the start signal and the pulse obtained from the MCP detector was used as the stop signal for the TOF measurements (section 2.5). The MCP detector could be moved along the beam axis over a distance of up to 16 cm (section 2.4) . The differences in flight time over these variations in the flight path were measured . Consequently, in these relative measurements, a precise knowledge of parameters

2. Experimental equipment, procedures and results 2.1 . Experimental setup The proton beam from the 100 kV accelerator was deflected (fig . 1) by a 90' double-focusing magnet through a pair of adjustable slits (section 2.3), and passed through an electrostatic quadrupole triplet lens, followed by a collimator of 0.50 mm diameter. The collimator was placed at a distance of 166 cm from the slits. The slits and the collimator served to define the beam axis, as well as to reduce the beam intensity (section 2.3). The beam then passed through a pair of electrostatic plates (20 cm length, 2 mm separation), another 0.50 mm diameter collimator (placed on the beam axis at a distance of 233 cm from the first collimator), a double microchannel-plate (MCP) detector (Chevron arrangement, fig. 2) and was finally stopped in a Faraday cup. In the electrostatic plates the beam was periodically deflected via a square-wave voltage (+ 15 to -15 V, see section 2.5) applied to the

DOUBLE MICROCHANNEL

-380V -1280 V -1680 V - 2590 V - 5000 V

ION BEAM

MESH

CARBON FOIL (-3480V)

Fig. 2. Schematic of the arrangement using a Chevron MCP as a timing detector. The distance between the two MCPs was 0.55 mm and that between the second MCP and the anode 2.8 mm. The overall dimensions of the arrangement were of the order of 10 cm each . The device was surrounded by a screening cup, designed to shield the Chevron MCP from electrons other than those produced in the carbon foil.

K. Neldner et al / Absolute energy calibration by TOF technique such as the time of the voltage crossover on the electrostatic deflection plates, the absolute length of the flight path, and the difference in time delay in the electronic systems for the start and stop signals was not needed . The vacuum in the beam tube was 7 X 10 -7 mbar. 2.2. Microchannel plate detector Microchannel-plate detectors have been described in detail in the literature [13,14] . In the passage of the proton beam (fig. 2) through a thin carbon foil (here: 3.5 ~Lg/cmz thickness, 4 mm diameter) secondary electrons are emitted [15]. The electrons are accelerated by the 890 V potential difference between the foil and a grid made of 97% transparent electroformed mesh. The electrons then enter a field-free region before being deflected by 90 ° by an electrostatic mirror (two meshes with a potential difference of 2410 V, both oriented at 45 ° to the ion beam direction, fig. 2), and finally strike the Chevron MCP (Hamamatsu F1551/03) . The transmission of the secondary electrons from the carbon foil to the MCP is about 87% . The double MCPs amplify [14] the electrons by more than a factor of 107 leading to a useful timing signal at the anode, with a leading edge of less than 1 ns and a pulse width of about 10 ns. The relatively short electron paths, the orientation of the carbon foil perpendicular to the proton beam direction, and the isochronous transport of the secondary electrons from the carbon foil to the double MCPs (i.e., nearly the same path length for all electrons) result in a small (< 70 ps) timing jitter in the output signal from the MCP [13,14] . 2.3. Intensity and energy resolution of the proton beam The MCPs can handle a maximum count rate of about 106 s-1 [14], which restricts the proton beam current in the setup of fig. 1 to less than 1 pA. This large reduction in beam current was achieved by (1) minimizing the ion-source output, (2) using tight apertures in the beam transport system (fig. 1), and (3) appropriately focusing the ion beam in the einzel lens located near the ion source [4]. Except for the TOF measurements at 10 keV, the electrostatic quadrupole triplet lens was turned off and its plates grounded. The slits near the exit of the 90 ° bending magnet (radius = 36 cm) had a width of 0.25 mm at all energies, except for E S 20 keV, where a width of 0.50 mm was used. From the known energy spread of the duoplasmatron ion source (FWHM = 3-4 eV, [16]), and the known ripple of the high voltage power supply (section 1), an energy resolution of the proton beam of AEb f 10 eV at E = 25 keV was estimated. In order to test this estimate, different parts of the proton beam were sampled by varying the magnetic field strength of the 90' bending magnet (e.g., until the beam intensity had

421

dropped by a factor of about 5 compared to the maximum). The TOF spectra obtained for these differing parts of the proton beam yielded an energy shift of 0Eb < ± 10 eV, confirming the above estimate. Thus, in spite of the tight slit widths, the TOF measurements lead to values for the proton energy representative of the whole beam, i.e., the slits mainly eliminate protons travelling on differing trajectories but having essentially the same energy . 2.4. Flight path variation The available space at the 100 kV accelerator strongly restricted the maximum possible flight-path length between the electrostatic deflector and the frame holding the carbon foil of the MCP (here: 1 < 240 cm) . Thus, for 1= 240 cm, the required precision of O1/1= ± 5 X 10 -4 (section 1) corresponds to Al= ±0 .120 cm. In principle, such a distance could easily be measured to the required accuracy (e.g., with laser techniques). However, foil wrinkling under ion-beam bombardment could lead to uncertainties as high, in extreme cases, as AI= ±0.1 cm. Furthermore, an even larger uncertainty could exist in the absolute determination of the geometrical "crossover point" in the electrostatic deflector (section 2.6). For these reasons, the MCP detector was mounted on a track and could be moved along the beam axis via a precision thread (2 mm per turn) over a distance of 16 cm. The reproducibility in the distance was tested via a precise mechanical setup [10], as well as via TOF spectra obtained at the same distance, leading to an uncertainty of A1= ±4 X 10-4 cm (i.e., A1/1= ±2.5 X 10 -5 for 1= 16 cm), which was sufficient for the present purposes . 2.5. Electronics At a proton energy of E = 50 keV, and for a change of flight path of l = 16 cm (section 2.4), the change in flight time is t = 48.481 ns, which must be measured with an accuracy of about At = f 0.024 ns (section 1). The voltage for the deflection plates was generated by a high-precision function generator (Philips PM 5134), which provides a square-wave voltage from + 15 to -15 V. With the plates connected, the change in polarity occurs within 30 ns. The variable (quartz-stabilized) frequency of the generator was measured with a 100 MHz counter/timer (Ortec, model 974) and found to be stable to better than ± 10-6. At the positive going change in polarity, the generator also provides a TTL compatible trigger signal, which was fed into a fast amplifier (FA, ESN Electronics, model FTA 810L), followed by a constant fraction discriminator (CFD, Ortec, model 934), to produce an appropriate timing pulse (with a leading edge of about 1 ns) for the start signal of the time-to-amplitude (TAC) converter. It

422

K. Neldner et al. / Absolute energy calibration by TOF technique 3k

TAC - SPECTRUM

w z z

a x

E=60keV

2k

â H z

--`

1k

FWMM=160ns

'"

0 CENTR010 = 52 75 ns

0

78

60

82

84

86

TIME Ins)

Fig . 3. Relevant section of a time-of-flight spectrum is shown as obtained with the TAC at a proton energy of E = 60 keV. The peak is centered at a relative flight time of 82 .25±0.01 ns and has a FWHM width of 1.80 ns . should be noted that only one sweep direction contributes to the TOF measurements, eliminating possible systematic differences between the two sweep directions. The signal from the MCP was passed through a FA followed by a CFD, the output of which provided the stop pulse for the TAC. The TAC was set at a nominal time range of 200 ns. The resulting spectra (fig . 3) were accumulated in a 4096-channel analyzer and stored on a disc . According to the supplier, the TAC (Ortec, model 467) has an inherent absolute time resolution of <0 .01% of the full time range (< 20 ps). The time calibration of the TAC was carried out with a pulse generator (Berkeley nucleonics Corp ., model BH-1), whose pulse was used both as the start and stop signal for the TAC. The stop signal was delayed via a combination of BNC cables (with a typical length of about 6 m each). The time delay of each BNC cable was measured in the following way: a single pulse (20 ns rise time, 50 ns fall time) from the pulse generator was fed into a CFD. The output of the CFD was fed into the counter/timer, and also amplified in an FA, delayed by 160 ns, and fed back to the CFD input. The frequency fo (= 4.4 MHz) of the pulse in this closed loop was measured with the counter/timer. Inserting a BNC cable in the closed loop led to a lower frequency fl (= 3.9 MHz for a 6 m long cable) . The time delay T of each BNC cable was then calculated from the relation T - f 1 - f1. Thus, this method does not require a precise knowledge of the cable length or of the signal speed in the cable. The frequencies could be measured with a precision of ± 3 Hz. Thus, by using combinations of these cables, an accuracy in the time calibration of the TAC of the order of f 1 x 10 -6 could be achieved, which was sufficient for the present purposes . In other experiments, a time calibrator (TC, Ortec, model 462)

was used for the TAC calibration, where the accuracy of the TC (accuracy = ±5 x 10 -5 , as quoted by the supplier) was checked prior to actual measurements by the method just discussed. The long term stability of the TC and the TAC was tested over a period of 10 h and found to be better than ±4 ps, more than sufficient for the present work . The electronics for both branches (i .e., FA and CFD) in connection with the TAC was tested, by adding a delay unit in one branch, for differing walk of the CFDs . For this test, a pulser signal (with fixed amplitude) or, alternatively, the signals from the MCP (with variable amplitude) were fed into both branches : the mean peak position in the TAC was the same within ±0 .004 ns, but the peak width increased from 0.08 ns (for the pulser signals) to 0.18 ns (for the MCP signals) . According to the supplier, the TAC has a differential nonlinearity of less than 2 x 10 -2 over the full range of 200 ns . This claim was verified experimentally (see above), where deviations in the differential dispersion up to ±5 x 10 -3 were observed . These deviations were reproducible to within ±2 X 10 -4 . Thus, the observed differential dispersions were used in the calibration of the TAC, with a mean dispersion of (4 .2844 ± 0.0005) X 10 -2 ns/channel. Although the proton flight times from the deflecting plates to the MCP detector exceeded the TAC range and changed for the different proton energies (table 1), all spectra could be taken in the same time range of 200 ns by an appropriate setting of the frequency of the Table 1 Summary of results a) ERC ETOF `) [keV] [keV] 9.97 b) 10.90 b) 29.88 39.84 49.79 59 .76 69.70 79.65 89 .60 99.53

10.04±0.05 19 .90±0.09 29.88±0.09 39.88±0.06 49.80±0.07 59 .55±0.12 69.65±0.19 79.54±0.07 89 .28±0.54 99 .58±0.29 weighted mean value =

ETOF

[eV]

- ERC

d)

70± 50 0± 90 0± 90 40± 60 10 ± 70 -210±120 -50±190 -110± 70 -320±540 50±290

(1 .5±26) eV e)

a) Proton energy of the 100 kV accelerator at Bochum (accuracy = ± 5 X10-4 ) as determined via the calibrated resistor chain (section 1). The slits after the bending magnet (fig . 1) had a width of 0.25 mm, except where quoted . b) Width of slits after bending magnet = 0.50 nun. `~ Results obtained from 24 individual measurements at each proton energy (section 2.6). d) Error includes only uncertainty in ETOF (column 2). `) External error (internal error = ±25 eV) .

K Neldner et al. / Absolute energy calibration by TOF technique voltage generator (from 0.79 MHz for E = 10 keV to 2.04 MHz for E =100 keV) . In this way, the start signal for the TAC was given by the next crossover of the plate voltage, following the one that was responsible for the actual beam pulse detected in the stop detector . For example, for E = 100 keV and for l = 240 cm, the flight time with respect to the "actual beam pulse" is t = 0.54 Ws ; with respect to the subsequent crossover (2 .04 MHz, or 0.49 ws later) it is t * = (0 .54 - 0.49) ws = 50 ns . This method required a highly stable frequency generator (see above), but avoided the difficulty of having to delay the start pulse for times of the order of microseconds with an accuracy of better than 1 ns .

1500

v w 0

W z

1000 500

0

0

-500

W

-1000

0

-1500

0

20

40 PROTON

2.6. Time-of-flight measurements From the tests just discussed, the time stability and accuracy of the electronic components should lead, at a given proton energy, to TOF measurements with an accuracy of about At/t = ± 1 X 10 -4 . However, from simple geometrical considerations, including the diameters and distances of the beam-defining apertures, it can be seen that, at the place of the last collimator (fig . 1), changes in the beam optics of the ion source (differing trajectories) could result in a transverse displacement of the beam by about ± 1 mm from the beam axis . Such displacements are not negligible compared with the maximum deflection at this collimator produced by the electrostatic plates (e.g ., 31 .5 mm for E = 50 keV) . Thus, the time peak in the TAC spectrum can shift by a time interval At, which is required for the voltage generator (rise time = 30 ns, section 2.5) to compensate for this displacement . For E = 50 keV and a displacement of 31 .5 mm (and 30 ns rise time), a ±1 mm displacement would lead to a time shift of i1 t = ± 1 ns . Long-term shifts of this order of magnitude were indeed observed during the series of measurements, and could not be reduced due to the restrictions in length of flight path at the 100 kV accelerator. Therefore, at each proton energy, 24 individual measurements of the velocity were performed and averaged to obtain a final mean proton energy and its associated error [10] .

3. Results The determination of the proton beam energy via the TOF technique (ETOF) is compared in table 1 and fig. 4 with that from the calibrated resistor chain (ERC). The quoted errors arise predominantly from the longterm shifts discussed in section 2.6 . On the average, the two determinations agree within experimental uncertainties, with a mean spread of f26 eV. Thus these measure-

42 3

60 ENERGY

80

ERC

(keV)

100

Fig. 4. The energy determination of the proton beam from the 100 kV accelerator in Bochum via the time-of-flight technique (ETOF) is compared with that from the calibrated resistor chain (ERC), where, for a better comparison, the deviation ETOF - ERC is shown as a function of ERC .

ments confirm the absolute energy determinations made via the calibrated resistor chain (section 1) . Acknowledgements The authors would like to thank the technical staff of the Dynamitron-Tandem Laboratorium (DTL) in Bochum for assistance during the experiments and B.P . Hippert (DTL) for the production of thin carbon foils. Advice on various technical aspects by F. Käppeler (KfA Karlsruhe) and M. Purschke (IKP Munster) is also highly appreciated . Finally, we thank C.A . Barnes (California Institute of Technology, Pasadena) for fruitful comments on the manuscript . References W.A . Fowler, Rev. Mod. Phys . 56 (1984) 149. C. Rolfs, H.P . Trautvetter and W.S . Rodney, Rep. Progr. Phys. 50 (1987) 1. S. Engstler, A. Krauss, K. Neldner, C. Rolfs, U. Schrilder and K. Langanke, Phys . Lett . B202 (1988) 179. [4] A. Krauss, H.W . Becker, H.P. Trautvetter, C. Rolfs and K. Brand, Nucl . Phys. A465 (1987) 150. J.B . Marion and F.C. Young, Nuclear Reaction Analysis (North-Holland, Amsterdam, 1968). [6] T. Freye, H. Lorenz-Wirzba, B. Cleff, H.P . Trautvetter and C. Rolfs, Z. Phys . A281 (1977) 211 . M. Uhrmacher, K. Pampus, F.J . Bergmeister, D. Purschke and K.P. Lieb, Nucl . Instr. and Meth . B9 (1985) 234 . [8] H.P . Trautvetter, K. Elix, C. Rolfs and K. Brand, Nucl . Instr. and Meth. 161 (1979) 173.