First analysis of GEM-TPC data

updated: November 7, 2001

A study of the first data taken with the 15 cm TPC with rectangular pads and P10 gas is summarized in this working document..
 

HV settings

Drift	5200?V
GEM	3150?V

 

Data runs

Run	Triggers	Filtered events
438	22532	2144
439	24580	2804
440	18145	1749
463	26645	2678
464	36111	3484
465	33242	3215
474	24997	2552

Triggers are provided by a cosmic telescope at a rate of about 0.4 Hz. A filter program selects only those with a signal in any channel exceeding 10 counts beyond pedestal level, which reduces the recorded event rate by a factor of 10. Note that the filter acceptance rate is larger in run 439. Events consist of 32 channels of 2000 8 bit samples in 5 ns time bins, and thus are about 64 KB. A 24 hour run takes about 200 MB.

The first filtered event is shown in this figure. The event in unusual in that it is well contained within the fiducial volume of the pads. The vertical scale is pedestal subtracted FADC counts from -50 to 10. For convenience, the plot shows the arrangement of pads rotated counterclockwise by 90 degrees. The event is a vertical muon, with the top being at the right. Small induced pulses are visible, in addition to the large direct charge pulses.

Analysis software

Data analysis is done using the program, tpcanal, version 0.3. The following commands are useful for interactive studies of the data:
 

some tpcanal commands

infile filename	specify midas event file
next	read next event
analize debug	show step by step analysis of data
plot [min [max [filename]]]	show event plot
help	show list of commands

The analysis program performs fits to the signals and fills an ntuple for further interactive analysis with PAW. The ntuple includes the following:
 

some tpcanal ntuple variables

variable	description
tr	time pulse rises to 50% of peak amplitude (ns)
tp	time of peak (ns)
vp	peak amplitude (FADC counts after ped subtraction)
tf	time pulse falls to 50% of peak amplitude (ns)
qp	integral of pulse from tr to tf
af	amplitude of pulse 500 ns after peak (after induction component has decayed)
an	af divided by average value of (af/vp)
ipp	problem bits for fitting pulses
tot	total charge in a row
edg	maximum charge on a row's edge (to define fiducial region)

A set of paw macros are available in tpc.kumac and tpcmon.kumac. The source code and ntuples are available on bragi, in the gmd account in the tpcanal directory. The programs are relatively easy to use. In the directory there is a link to the data directory, rawdata, so to specify data from run 438, enter rawdata/filt00438.mid. Ntuple files are also found in this directory (filt00438.rz for example).

General properties of the data samples

The trigger event numbers are shown vs time since beginning of run 438 in this figure. There are a few instances where the DAQ cpu clock looses a few hours.

The distribution of rise times is shown in this figure. Runs are shown as red: 438, black: 439, and blue: 440. The widths of these distributions are consistent with the expected drift velocity (50 microns/ns) over a total drift of about 15 cm. The last run shows a slightly smaller width, which may indicate a change in the gas properties. A scatter plot of rising edge times versus time, shown in this figure, indicates that the drift velocity is not constant. The drift velocity appears to vary by as much as 20%.

The peak amplitude (deduced from fitting the peak region to a quadratic function) distribution is shown in this figure. The gain could be increased by a factor of 2 without causing significant saturation. The lower edge cutoff results from the requirement that the fits are only performed if there is pulse exceeding 5 FADC counts.

The FWHM pulse distribution (ie. tf - tr) is shown in this figure. A clear distinction is seen between short (induced) pulses and the long direct charge pulses. The fit to the short pulses, gives a mean of 180 ns. This is consistent with the time required for the charge clouds to completely drift through the final 5 mm GEM gap. This time required depends on the drift velocity and the longitudinal diffusion. The dependence on the diffusion is shown in this figure, where the FWHM distribution is shown for different ranges of tr.

A comparison of the various channels is shown in these figures. There is a significant problem with the pre amp used to readout pad #2. The time constant is significantly different from the other channels, as can be seen in the figure comparing the tf distributions for the various pads. Fortunately the pad will not be used directly for tracking studies, since it is an outer pad. Pad #6 has a large tail of pulses with tr beyond the cutoff of about 6000 ns.

Gain studies

The total charge collected on each row can be used as a measure of the gas gain. To ensure that the active pads in a row collect all the charge in that row, it is required that the pads on the two ends of the row have no charge themselves. This figure shows the distribution of total row charge for runs 438, 439 and 440 (red, black, and blue). The average total charge (in ADC counts) does increase somewhat during the early runs. The average total charge is shown vs time in this figure. The gas gain is stable to about 10% over a period of 140 hours. The total charge seen in each row is shown in this figure. The observed variation of about 5% indicates that the pad to pad gain variation is less than about 10%.

Tracking studies

Track fitting to the data is performed to understand the resolution properties of the TPC. This figure shows the coordinate system for the track parameters. The track is defined by the coordinate (x₀,0,z₀), the azimuthal angle, phi, and the angle in the y-z plane, psi. It is useful to define a local offset from the center of each pad, b. Tracking studies are performed on events with contain signals in all rows, and in which the edge pads on all rows contain less than 10% of the total charge collected by that row. Track fitting is performed in y-z and x-y separately. No channel to channel calibrations have yet been performed.

y-z tracking

Pads that have a signal peak of 5 or more ADC channels below the pedestal are used as hit candidates. The pulse arrival time is defined as the time that the rising edge reaches 50% of the peak pulse height, (tr). Since the cosmic telescope triggers the FADC in common stop mode a fixed delay after the trigger, the arrival time is linearly related to the z coordinate. Pulses in a given row (common y coordinate) are combined to form a single z coordinate for that row.

There is an unexplained systematic time dependence on the amplitude of the pulse on a pad, which is corrected for. As usual, the pulse amplitude is estimated using a fit to the pulse 500 ns after the peak of the pulse (an). This figure shows the difference between a row average tr using large pulses only (those with 50 < -an < 200) and the tr for all pulses as a function of the average pulse amplitude an. Pulses with amplitudes less than about 50 counts arrive earlier than larger amplitude pulses by as much as 90 ns. An exponential fit to this data is used to define a corrected rising edge time, trc. This effect needs to be better understood, and perhaps another algorithm be used to define the pulse arrival time.

Each row z coordinate is defined by an amplitude weighted average of the corrected pad times in that row. The row y coordinate is simply defined by the centre of the pad row. An unweighted linear fit of (z,y) coordinates is performed. The distribution of z₀ and psi are shown in this figure. (A time offset of 2000 ns and drift velocity of 50 micron/ns is assumed for these plots). The angle psi has a standard deviation of 0.2 radians (11 degrees), so most of the tracks are nearly vertical.

To estimate the resolution of a single row z measurement, the linear fit is repeated without the row, and the z coordinate from the fit is compared to the z coordinate of the row. The difference between the row and fit z coordinate is shown in this figure, with a standard deviation of 860 microns. Accounting for the fact that the track fit is determined from 4 measurements, the estimated z resolution for these events is 770 microns. This is significantly larger than what would be expected from the longitudinal diffusion. There are likely residual effects from the large correction applied as a function of pulse amplitude.

The z resolution for 4 different bins of z₀ are shown in this figure. As expected, there is no evidence that resolution is dominated by diffusion. Further studies are necessary to determine the reason for the larger than expected z resolution.

x-y tracking

As in the y-z track fit, each row is used to define a single hit on a track. For linear collider TPC designs, it is important to correctly deal with situation where only two pads within a row collect charge. For this case it was shown in our space point resolution studies that it is incorrect to use a linear charge weighted centroid estimate. In those studies, a charge cloud shape of a 2D Gaussian was integrated over the pad areas to estimate the centroid of the charge cloud, given the observed charge fractions in each pad.

A logical extension for the tracking analysis is to use a model with a uniform line of charge with the transverse distribution in the x-y plane given by a Gaussian. The integration of such a line charge over a rectangular pad is shown in this figure. The charge fluctuations along the length of the track are not included in the model. The observed charge fractions in the pads is unaffected by such fluctuations for track angles near phi=0.

For each row, charge fractions in each pad are calculated and compared to the expected charge fractions given by the integrals, I. The track fit is performed by minimizing the chi**2 difference of the observed and expected charge fractions in the 5 rows, while varying the track parameters, x₀ and phi, and the transverse standard deviation of charge, sigma. Since the tracks are mostly vertical, a single choice for sigma for all rows is a reasonable approximation. The chi**2 is summed only over pads that are observed to have at least 2% of the row charge. The absolute uncertainty in the charge measurement from the pads is assumed to be the same for all pads.

This figure shows the result for x₀ and phi. These track parameters are limited in range due to the fidicual volume cut described above. This figure shows the fitted value for sigma, the transverse scale of the line charge, as a function of drift time. It follows the expected form of diffusion. Assuming  a drift velocity of 50 microns/ns, the transverse diffusion constant is 0.142 sqrt(mm) or 0.045 sqrt(cm). The diffusion constant calculated by Magboltz is 0.065 sqrt(cm). The diffusion for tracks at the edge of the GEM is about 0.52 mm. The GEM system has a 7mm gap which, with diffusion constant of 0.065 sqrt(cm), would provide a diffusion at this point of 0.54 mm. The diffusion in the GEM itself matches the expectation, but this is not the case in the drift volume of the TPC.

To estimate the transverse track resolution from a single row, events are fit by excluding the row to determine x₀, phi, and sigma. The data from the single row is then fit with only x₀ free, while phi and sigma are fixed to the values determined from the fit to the four other rows. The chi**2 value from the 4 row fit is used to discard events with poorly measured reference tracks. This figure shows the difference between the single row and 4-row fit x₀ track parameter for different drift distances. For distances beyond 10 mm of drift, it is clear that the resolution is diffusion limited. For the sample of events having z₀ within 10 mm of the GEM foils, the average track resolution is about 200 microns (remembering to divide the fitted standard deviations by sqrt(1.25)).

This figure shows the resolution when the single row x₀ coordinate is estimated by the simple linear centroid method. The resolution is significantly worse for the smallest drift distances. Once again, this demonstrates that the linear method of defining hit centroids should not be used for precision track measurements.

The Gaussian model requires some knowledge about the transverse width of the charge clouds. The track fits described above, fit for this parameter (sigma) on an event by event basis. Alternatively, the value for sigma can be set as a function of the drift distance. This figure shows the transverse resolutions as determined when the value of sigma is set in this way. The resolutions are similar to the case where sigma is fit for each event.

For further studies of resolution effects, we are limited to the small sample of events in the first 10 mm of drift volume. The sensitivity to non-uniform ionization along the length of the track is greater for tracks that are further from phi=0 (the so-called track angle effect). This figure compares the resolution for tracks with abs(phi) < 0.05, with 0.05 < abs(phi) < 0.15,  and with abs(phi) > 0.15 (all within the first 10 mm of the drift volume). There is a very strong track dependence on the resolution. For the first phi bin, a resolution of about 100 +/- 15 microns is seen. The other two bins in phi have resolutions consistent with each other of about 250 microns. It is remarkable that 100 micron tracking resolution can be achieved in this first analysis of the data, without channel to channel gain calibrations applied. There are only 10 events in this restricted sample, however. Gas with a lower diffusion constant should be used in future data taking in order to increase the fraction of events that can contribute to precision tracking studies.

The resolution depends on the number of primary electrons produced. This figure compares the resolution for events with total row charge collected below and above 50 FADC bins. To increase statistics, events within the first 20 mm of drift are considered. As expected the resolution is better for the rows with greater collected charges.

The following table shows a sample of events with small drift distance and small track angle, phi. The track plots show x-y, y-z, and x-z views of the data. The size of the box in the x-y view is proportional to the charge collected by that pad. The bottom right figure shows the charge fractions observed in each of the 5 rows (histogram) and the result of the fit by the Gaussian line model (red squares). Squares are only shown for pads that observe to collect at least 2% of the charge.
 
 

Some events with drift length < 10 mm and abs(phi) < 0.05

run	event	event plot	track plot
464	1441	event	track
464	7247	event	track
465	1816	event	track
465	17357	event	track
465	26637	event	track
465	31238	event	track