DESIGN OF A 10 NM ELECTRON COLLECTOR FOR A TRACK-

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1 DESIGN OF A 10 NM ELECTRON COLLECTOR FOR A TRACK- NANODOSIMETRIC COUNTER L. De Nardo 1, A. Alkaa 2, C. Khamphan 2, P. Colautti 3, V. Conte 3 1 University of Padova, Physics Department, via Marzolo 8, I Padova (Italy) 2 Centre de Physique des Plasmas et de leurs Applications de Toulouse, U.M.R. du CNRS n 5002, Université Paul Sabatier, 118 Route de Narbonne, 31052, Toulouse Cedex 04, France 3 INFN Laboratori Nazionali di Legnaro, viale dell Università 2, I Legnaro, Padova, Italy Running title: 10 NM ELECTRON COLLECTOR This is a pre-copyedited, author-produced PDF of an article accepted for publication in Radiation Protection Dosimetry following peer review. The version of record [Radiat Prot Dosimetry (2004) 110 (1-4): doi: /rpd/nch113] is available online at:

2 DESIGN OF A 10 NM ELECTRON COLLECTOR FOR A TRACK- NANODOSIMETRIC COUNTER L. De Nardo, A. Alkaa, C. Khamphan, P. Colautti, V. Conte ABSTRACT Recently we have developed a track-nanodosimetric counter, that is a gas detector able to measure the distributions of electrons induced by a charged particle in nanometric volumes of tissue equivalent matter, positioned at different distances from the track. 20 nm and 24 nm sites were defined by means of an electron collector, that is a system of electrodes enclosing an almost wall-less cylindrical volume. In this paper we present the design of a new electron collector, able to simulate a volume as small as 10 nm in diameter.

3 INTRODUCTION Effects of radiation are primarily determined by what happens in individual small volumes representative of DNA segments. Such sites are so small that the interactions due to the radiation are very few and it is necessary to consider the stochastics of the number and nature of primary interactions and of secondary processes in order to understand the subsequent biological effects. Track-nanodosimetry has the objective to investigate the stochastic aspect of ionization events in particle tracks, by measuring the ionisation distributions induced by a charged particle in nanometric volumes of tissue equivalent matter, positioned at different distances from the track. Recently we have developed a track-nanodosimetric counter that is a gas detector able to measure the distributions of ionization events induced by a charged particle in nanometric volumes of tissue-equivalent matter, positioned at different distances from the track (1). The counter was used to measure the probability of the formation of ionization clusters by primary 244 Cm -particles at 5.4 MeV in sites equivalent to 20.6 nm and 24.0 nm (2). For these volumes, the mean total counting efficiency for single electrons was evaluated to be about 20% and 28% respectively (1). The consistency of our track-nanodosimetric measurements was checked by comparison with suitable ionization-yield distributions determined by Monte Carlo simulations, obtaining a satisfactory agreement (2). Both experimental data and Monte Carlo calculations suggest that ionization fluctuations in nanometric volumes inside the δ-ray cloud of an α-particle are invariant with the distance from the track. Unfortunately, our findings could not be directly compared with other experimental data at the nanometric level obtained with detection systems based on single ion

4 counting (3,4), as in these devices the diameter of the sensitive volume () is generally smaller than 10 nm. To overcome this limitation, we are working at reducing the simulated size of the of our detector. This will allow also to investigate whether the measured invariances also exist at smaller distances from the track. Unfortunately, with our present version of the track-nanodosimetric counter, we can not simulate target volumes equivalent to 10 nm, as the gas pressure is too low to allow single electron detection. Besides, at such low pressure, the electron collection efficiency is very low (about 5%). Therefore, to simulate a 10 nm, we need to design a new electron collector (EC) for our counter, with smaller physical size. In this paper we present the design of a new EC, simulating a cylindrical as small as a histone (11.7 nm 5.8 nm) and the results of electron collection efficiency calculations. THE TRACK-NANODOSIMETRIC COUNTER In figure 1 the draft of the experimental set-up for track-nanodosimetric measurements is shown. Two collimators positioned in front of a solid-state detector (SSD) define the primary particle track, with respect to which the detector can be moved using a micrometric screw. The detector consists essentially of an electron collector (EC) and a single electron counter (SEC), joined together through a system of electrodes. The whole detection system is immersed in the counting gas. The EC is a system of electrodes that encloses an almost wall-less cylindrical volume. Electrons created inside this volume, the of the counter, are transferred into the drift column of the SEC and are detected one by one, by using a multi-step avalanche chamber (MSAC). More details about the apparatus can be found elsewhere (1).

5 ELECTRON COLLECTOR RATIONALE The EC has to transfer the sub-ionization free electrons, emerging from the ionization events, to the SEC. However, the SEC has a detection efficiency less than one for cluster size greater than about 15 electrons (2). In order to assess the loss of efficiency for big clusters, the new EC is a double cone with up-down symmetry with respect to the centre. By changing the set of voltages applied to the electrodes composing the EC, it is possible to invert, inside the, the electric field component parallel to the axis. In this way it will be possible to measure electrons alternatively, with the same collection efficiency, either with the SEC or with a proportional counter (PC) connected to the other extremity of the EC. By comparing, in different ionization density track position, the mean cluster size measured with the SEC and the PC mean signal, we should be able to evaluate experimentally the loss of efficiency in measuring big clusters. ELECTRON COLLECTOR DESIGN Ionization events take place both inside and outside the. The EC has to collect the -inside electrons and, at the same time, it has to prevent the collection of -outside electrons. Therefore, the electric field inside the must have a strong vertical component. On the contrary, the electric field outside the must have an electric field component transverse to the axis to minimize the electron diffusion from outside to inside the. Moreover, the probe volume must be transparent to the primary particle as well as to fast electrons emerging from the particle track. To optimise the electric field configuration, the EC was designed with the help of the general purpose partial

6 differential equation solver FlexPDE TM. It was used to solve the Laplace equation with a general finite-element algorithm. In figure 2 the radial section of the EC is drawn. The EC consists of two identical truncated opposed cones, which enclose the. Each of them is composed of 9 different electrodes. One truncated cone will be connected to the SEC. The other truncated cone will be connected to a parallel plate proportional counter (PC). The distance between the two cones, and hence the height of the, can be changed by a micrometric screw. The internal diameters of the two extremities of the truncated cones are 1.2 mm and mm respectively. The wall-less is mainly shaped by 4 electrodes, they are the first internal electrodes and the two external electrodes of the two truncated cones. The thickness of the first internal electrodes is 0.1 mm, that of the external electrodes is 0.5 mm. The thickness of the remaining 7 electrodes of each of the two cones is 0.5 mm, that of the insulators is 2.0 mm. All the electrodes have rounded edges, to avoid high electric fields in their neighbourhood. In figure 3 we have represented a typical equipotential line plot in the collecting region of the detector. The shape of the equipotential lines suggests that electrons created inside the will be attracted, by the electric field, towards the collecting cone while the electrons created outside the will be pushed away (the arrows indicate electron drift lines). COLLECTION EFFICIENCY CALCULATIONS The efficiency of the collector to transfer electrons to the SEC was calculated with a Monte Carlo code. Details about the code can be found elsewhere (1). The

7 software FlexPDE TM was used to provide to the Monte Carlo code both the electric field inside the counter and the boundaries of the domain in matrix form. Eventually, the best EC configuration and the best set of electric biases, which maximises the efficiency, were determined. Calculations were performed with C 3 H 8 gas at pressures of 267 Pa and 457 Pa (at 25 C) considering an initial energy of the electrons of 2 ev. At these pressures the scaling factors for getting target sizes or distances on a nanometric scale are 4.87 nm/mm and 8.34 nm/mm, respectively, if a material of unit density is assumed. This corresponds to simulated diameters of the of 11.7 nm and 20.0 nm, respectively. Figure 4 shows the electron collection percentage efficiency map of the with diameter and height respectively of 11.7 nm and 5.8 nm, after having optimised all the electrodes voltages. The origin of the co-ordinates is the centre of the bottom of the. As expected, the collection efficiency is not uniform inside the, it is a function of r and z. The average efficiency of the has been calculated by integrating on r and z: rdrdz (1) rdrdz where the limits of the integrals are the dashed lines that mark the in figures 3 and 4. The average collection efficiency of the is 31% at a gas pressure of 267 Pa. Outside the marked border, the collection efficiency falls to values lower than 5% within about 2 nm. About 76% of the electrons collected by the probe come from the.

8 At the same gas pressure of 267 Pa, but by increasing the height of the, in order to get a cylinder with equal height and diameter of 11.7 nm, decreases to about 24%. This is due to the reduced focusing capability of the electric field through the cone hole with increasing height of the. For the same physical dimensions of the, but with increasing gas pressure (457 Pa), corresponding to a 20 nm 20 nm cylinder, the average collection efficiency increases to about 36% (for the same simulated size we got with our old EC a mean efficiency of about 25% (2) ). CONCLUSIONS With the help of a partial differential equation solver software and of a Monte Carlo code, we have designed a system of electrodes able to collect the electrons released in a very small cylindrical sensitive volume with fixed diameter but variable height. The total single electron efficiency of the track- nanodosimetric counter can be considered to be a product of three factors: the efficiency of electron transfer from the into the detector, the efficiency drift of electron transfer through the drift column and the detection efficiency MSAC for single electrons at the MSAC (2) : drift MSAC. In this paper we have calculated for the new electron collector in propane gas at 267 Pa and 457 Pa, corresponding to diameters of 11.7 nm and 20 nm respectively. For a with a diameter and a height of 11.7 nm 5.8 nm the average collection efficiency for single electrons,, was about 30%. For with equal height and diameter, is about 25% and 35% respectively for 11.7 nm and 20 nm sites. In the future, with a modified version of our Monte Carlo code, we will optimise the fitting of the electron collector to the drift column of the detector

9 and we will calculate drift. Besides, we will determine experimentally the detection efficiency ε MSAC at the different pressures (i) by acquiring a gain distribution spectrum of single electrons, (ii) by fitting the spectrum with a Polya distribution, and (iii) by the evaluation of that fraction of the Polya distribution which is below the detection threshold of the counter. The conditions of measurement will be chosen in such a way to reach the best compromise between maximization of ε MSAC and minimization of the production of secondary avalanches (afterpulses). The values of drift and MSAC determined with our present version of the detector were 84% and 98% respectively (1) and we expect to obtain similar values even with the new version. We have already shown that the small and non-uniform efficiency of our tracknanodosimetric counter is not an obstacle to verify the existence of a region, in the track produced by an -particle, of invariant mean conditional cluster size and relative variance (2). To investigate the presence of these invariant features for other charged particles of radiobiological interest, the new EC will be mounted in an upgraded version of our detection system which will be installed at the TANDEM_ALPI accelerator at the Legnaro Laboratories. However, to get a complete quantitative experimental picture of ionization cluster size formation by charged particles, the full reconstruction of cluster size distributions at 100% efficiency would be necessary. For this reason, we are studying the use of Bayes'theorem to perform reconstruction of cluster size distributions at 100% efficiency from experimental data obtained from with low and not uniform efficiency (5-6).

10 REFERENCES 1. De Nardo, L., Alkaa, A., Khamphan, C., Conte, V., Colautti, P., Ségur, P. and Tornielli, G. A detector for track-nanodosimetry. Nuclear Instruments and Methods in Pyhisics Research A 484 (1/3), (2002) 2. De Nardo, L., Colautti, P., Conte, V., Baek, W. Y., Grosswendt B. and Tornielli G. Ionization-cluster distributions of α-particles in nanometric volumes of propane: Measurement and calculation. Radiation and Environmental Biophysics 41, (2002) 3. Pszona, S., Kula, J., Marjanska, S. A new method for measuring ion clusters produced by charged particles in nanometre track sections of DNA size. Nucl Instrum Methods Phys Res A 447: (2000) 4. Shchemelinin, S., Garty, G., Breskin, A., Chechik, R., Schulte, R.W.M. Ioncounting nanodosimetry: a new method for assessing radiation damage to DNA. Nucl Instrum Methods Phys Res A 477: (2002) 5. Lesimple, M., De Nardo, L. and Grosswendt B., Bayesian analysis of data: reconstruction of track structure at 100% detection efficiency for a tracknanodosimetric counter. Radiat. Prot. Dosim. 103, (2003) 6. De Nardo, L., Lesimple, M., Canella, S., Grosswendt, B., Reconstruction of cluster distributions at 100% detection efficiency for a track-nanodosimetric counter through a Bayesian analysis. Radiat. Prot. Dosim. This issue

11 Figures Fig.1 Schematic view (not to scale) of the measuring principle and of the main components of the track-nanodosimetric counter. The charged particles of a collimated beam pass the sensitive volume () and are detected by a solid-state detector (SSD); the sub-ionization electrons produced by each particle within the are collected, through the electron collector (EC), to the single electron counter (SEC), which consists of a drift column and a multi-step avalanche chamber (MSAC). The EC can also transfer the electrons down to a proportional counter (PC) (see text).

12 Fig.2 A radial cross-section of the electron collector. The 0 co-ordinate for R is on the rotational axis. Electrodes are in black and the insulators are in white. The sensitive volume zone has been enlarged. The charged particle is supposed to cross the sheet of paper perpendicularly at half the height.

13 Fig.3 Equipotential line plots inside and just around the, plotted with a 0.5 V step. The arrows indicate electron drift lines. The dashed lines point out the volume in which the average efficiency is calculated. The height of the is equal to its radius (1.2 mm). The 0 co-ordinate for R is on the rotational axis, the 0 co-ordinate for Z is on the bottom of the.

14 Fig.4 Calculated electron collection efficiency map in propane at 267 Pa corresponding to the situation of Fig.3. The equi-efficiency lines are plotted with a 5% increment. The dashed line points out the volume in which the average efficiency is calculated.