A Measurement of Photon Production in Electron Avalanches in CF₄

To measure the number of electrons in the avalanche, the amplitude of the wire signal spectroscopic amplifier pulses must be correlated to an absolute number of electrons. This is accomplished using a 10 pF test input on the integrating preamplifier. A known voltage placed across this capacitor translates into a known charge propagated through the electronics chain. A quadratic polynomial fits the calibration data best, corresponding to a small non-linearity in the preamplifier; a typical calibration is $N_{e^{-}}=(2.68\times~10^{6})V_{sa}^{2}+(4.50\times~10^{7})V_{sa}+(4.62\times~10^{6})$, where $N_{e^{-}}$ is the number of electrons and $V_{sa}$ is the spectroscopic amplifier output. Thus, a 4 V signal in the amplifier corresponds to 2.28$\times 10^{8}$ electrons.

The number of photons is measured with a PMT, which is calibrated with a known light source. For this calibration, a green (565 nm) LED is placed in the apparatus next to the slit in the proportional chamber. The LED is pulsed with a narrow (100 ns) square wave at 1 kHz. The voltage of the square wave is adjusted until a single photon from the LED is detected by the PMT in about 10% of pulses, and zero photons the remainder of the time. Poisson statistics dictate that at this 10% occupancy, a two photon signal would be observed 0.5% of the time. This one photoelectron signal is fed through the PMT electronics chain and read out in the same way as a photon signal from an avalanche. The distribution of the number of events vs. PMT signal voltage is fit with two gaussians, corresponding to a pedestal and a signal peak. The mean of the signal peak corresponds to one photoelectron, and typically is 5 mV after pedestal subtraction. This calibration was repeated with 5% and 1% occupancy, and the results were consistent with the calibration at 10% occupancy. Thus, a 20 mV PMT signal corresponds to 4 photoelectrons.

The slit in the proportional tube only captures a small fraction of the isotropic light that is emitted in the avalanche at the approximate location of the interaction point of the Fe-55 X-rays. To measure this effect, the LED is attached to an optical fiber, which is placed in the opening for the Fe-55 source. The length of the fiber is adjusted so that the end of the fiber is as close to the central wire as possible, since the bulk of the avalanche occurs within one wire radius of the wire’s surface. The PMT is placed as shown in Fig. 1, and signals are read out through the entire electronics chain. Then the end of the fiber is affixed directly to the face of the PMT and again the signals are read out. The ratio of the mean PMT signal distribution from the fiber inside the tube to the fiber on the PMT gives a solid angle and transmission coefficient of $0.00073\pm 0.00012$. The error on this number reflects the variation over several trials.

However, this value must be slightly corrected since the optical fiber is not isotropic, but rather directs most of the light in one direction. This correction is done using a simulation which bounces photons off of the reflective surface of a cylinder. The difference between light tightly focused in one direction and isotropic light gives rise to a correction of +5%. Dividing by the value of acrylic transmission at 565 nm (see Section 3.4) gives the value of the solid angle acceptance alone. No correction is made for the transmission of the quartz window, as the window had been removed when this measurement was made. Thus, the final value for the solid angle acceptance is $0.00083\pm 0.00017$, where the error includes the measurement error, along with a 5% error related to the anisotropy and a small error from the transmission correction. A calculation of just the angle subtended by the slit gives a solid angle factor of 0.0002. This calculation is confirmed by setting the reflectivity of the simulation to zero.

Light from the avalanche is attenuated by the quartz window and the acrylic vacuum vessel cover before reaching the PMT. The transmission of both materials is measured with a Jobin-Yvon 1250M spectrometer using an ultraviolet-sensitive Hamamatsu R928 multialkali PMT [13], with an incandescent lightbulb providing a continuous input spectrum.

The measured transmission curve of the acrylic is shown in Fig. 2.

The measured quartz transmission curve is shown in Fig. 3. This result is startling because the transmission is so low; the normal transmission of quartz is around 0.95 across all wavelengths of interest. This piece of quartz, however, had a crystalline growth on it, which accounts for the severely attenuated transmission. The level of growth was assumed to be constant over one month of data collection.

The PMT response is also wavelength dependent; Fig. 4 shows the quantum efficiency of the photomultiplier tube [12].

To report the ratio of photons to electrons in an apparatus independent way, the observed number of photons must be corrected for the fraction of the total spectrum that is observable in this particular apparatus. Note that the spectrometer replaces the PMT in Fig 1; that is, the spectrum is measured through the same slit used in counting photons from the avalanche. Fig. 5 shows the measured emission spectrum. The spectrum is normalized to unit area, because the fraction of observable photons depends only on the shape of the spectrum, not its normalization. The spectrum was taken in 2 nm steps with the same spectrometer used in the transmission measurements. The spectrum has been corrected for second order diffraction at wavelengths above 400 nm; below 200 nm, oxygen in the air absorbs any photons, and so light from 200 to 400 nm has no second order component. The light intensity above 400 nm is given by the equation

, where $f$ is the fraction of second order light, and $QE(\lambda)$ is the wavelength dependent quantum efficiency of the spectrometer phototube. Since the quantum efficiency is known, if $f$ is known, then the above equation can be solved for $I^{true}(\lambda)$. The value of $f$ can be measured by taking the spectrum of an ultraviolet source both in the UV and in the visible, with and without a filter with a cutoff near 400 nm, and then comparing the intensity in the visible to that in the UV, after correcting for the transmission of the filter. In this spectrometer, $f=0.25\pm 0.1$.

This is the first measurement of this spectrum between 200 and 800 nm. Note that 58% $\pm$ 6% of the spectrum is above 450 nm. This is particularly interesting, since the quantum efficiency of most CCDs turns on around 450 nm and peaks around 600 nm, indicating that CCD readout is well-matched to the CF₄ spectrum. See Ref. [14] for an explanation of the excitations of the CF₄ molecule that give rise to the 300 nm and 630 nm peaks. Note also a few transition lines in the spectrum; the origins of these lines are not described in the literature, and could be a point of further study.

The spectrum measured by the PMT in the proportional tube apparatus, shown in Fig. 6, is computed within each wavelength bin with the formula

where $I_{spectrum}$ is the total CF₄ spectrum, $T_{acrylic}$ is the transmission through acrylic, $T_{quartz}$ is the transmission through quartz, and $QE_{PMT}$ the PMT quantum efficiency. By integrating this spectrum and comparing with the raw CF₄ spectrum, an overall wavelength dependent correction factor of $0.0035\pm 0.0002$ is found. Figs. 5 and 6 do not show error bars, but the statistical error on the spectrum, as well as the errors contributed from background subtraction and multiplying by the quartz and acrylic transmission curves are included in finding the correction factor error. Typical relative errors on the raw spectrum are 30% and on the convoluted spectrum are 50%. Because the integral is performed as a sum, the relative error on the final correction factor is significantly reduced, because of the properties of propagation of errors in addition. Table 2 shows the relative size of the corrections to the photon measurement. Combining all of these corrections gives

where $C_{\lambda}$ is the wavelength dependent correction factor, $C_{sa}$ is the solid angle correction factor.

The number of electrons and photons in the avalanche were measured for a range of pressures and wire voltages. Fig. 7 shows the number of electrons (solid circles) and photons (open circles) produced in the avalanche as a function of voltage at 180 Torr; Fig. 7 shows the same as a function of pressure for 2325 V. Comparing the two processes, it is clear that the photon emission and the electrons production are linked, as they show similar functional dependance on the two variables of wire voltage and pressure.

The interpretation of the data, beyond the general trend that the avalanche multiplication increases sharply with voltage and decreases sharply with pressure, is difficult. CF₄ scintillates in ultraviolet, and the UV photons striking the side of the proportional tube eject electrons, which create secondary avalanches; as a result one Fe-55 decay can produce up to 10 avalanches. Since the number of avalanches is not constant for a given wire voltage, this makes it difficult to calculate the gain, $N^{avalanche}_{e^{-}}/N^{primary}_{e^{-}}$. An interesting side-effect of this phenomenon is an easy way to estimate the drift velocity in CF₄. Since the pulses come an average of 105 ns apart, and the radius of the tube is half an inch, the corresponding drift velocity is approximately 12 cm/$\mu$s. This is in good agreement with [15], at the field near the edge of the tube, 35 kV/m, at 180 Torr (1.48 kV/cm/atm).

While the gain of the gas is expected to vary with pressure and voltage, the ratio of photons to electrons should be invariant, as it is an intrinsic property of the gas. The data validates this hypothesis, and therefore all of the data can be combined to calculate the ratio. Fig. 8 shows the number of photons as a function of the number of electrons for all data after all calibrations and corrections have been applied. A first-degree polynomial describes the data well; this is the functional form used to fit the data. The fitted line is also constrained to pass through the origin, corresponding to a detector limit of zero photons emitted when zero electrons are present. The slope of this line, $0.34\pm 0.04$, gives the number of photons emitted per electron in the avalanche. This ratio is measured over the range of 140-180 Torr and 2150-2425 V.

The largest source of uncertainty in this measurement comes from the variations of experimental conditions between runs. This variation can come from a number of factors, the most prominent of which are variations in gas pressure and contamination. The measured leak rate of the vacuum vessel is 5x10^-6 Torr/L$\cdot$s, with the result that taking data over the span of four hours leads to contamination of 0.2% of the CF₄ with air. Furthermore, different levels of contamination before filling the vessel with CF₄ can affect the run to run performance. Local temperature and humidity variations can also affect the level and nature of contamination, as well as the performance of the PMT.

The error resulting from the variation between runs is taken into account in the error bars of Fig. 8. A scatterplot of $N_{\gamma}$ vs. $N_{e^{-}}$ is made from all the data. Then a profile plot is created using the spread of the data points in each bin of the histogram when calculating the errors, instead of the root mean square (RMS). The reason for this choice is that in each bin of number of electrons, several data sets are combined. If only one data set were used to make this plot, the projection of this bin onto the y-axis (number of photons) would be gaussian, and the error on the mean would be the appropriate error. However, since the projection is, in fact, non-gaussian, the spread better describes the error on the mean. Typical errors are 50%. The errors introduced from the solid angle and wavelength-dependent factors are then also included in the error bars of Fig. 8, added in quadrature with the error from the spread. Note that the correct choice of error when making the plot has a significant effect on the error of the fit; using the spread instead of the RMS increases the error on the photon to electron ratio by approximately a factor of two.

The measured ratio of photons to electrons, 0.34 $\pm$ 0.04 is in agreement with the Pansky et. al. measurement of 0.3 $\pm$ 0.15 [9], but improves on the relative error by a factor of five. Furthermore, the Pansky measurement was made at 10 Torr, and this measurement was made at 140-180 Torr, which is more typical of current and proposed experiments using CF₄ as a detection technique for dark matter.