MC simulation for Solenoidal Large Intensity Device (SoLID)

Introduction

Motivation

A High Intensity, Large Acceptance Spectometer (tentatively, HILAS) is considered for a long-range plan at 12 GeV in Hall A.

The main purpose is to measure the Parity Violation effects in DIS (PVDIS) at X_Bj>0.6 with an accuracy of about 1%. Due to a small production cross section this spectrometer has to run at a very high luminosity (L≅5.4·10³⁸ cm^-2s^-1= 540 pb^-1s^-1) on hydrogen, while providing an acceptance of ≅50% in the angular range of interest. No existing or planned device at JLab can be used for these experiments.

The first option considered is a magnetic spectrometer based on a large solenoid. It is tentatively called Solenoidal Large Intensity Device (SoLID). The target is located in the middle of the solenoid. In order to improve the ratio of the DIS signal to various backgrounds a system of baffles has to be designed and accurately positioned between the target and the detectors.

Another application of SoLID would be relatively low luminosity (L≅10 pb^-1s^-1) Semi-Inclusive DIS (SIDIS) experiments with polarized ³He targets. The target should be located upstream of the solenoid in a low field area. Hopefully, no baffles are needed in this case.

PVDIS kinematics

The goal is to measure the PV asymmetry in DIS with an accuracy of about 1% at X_Bj>0.6 and W²>4 GeV². The maximum beam energy is 11 GeV. The PV asymmetry is about:
A ≅ 3·G_F/(5·πα√2)·Q²· (a₁+a₂·(1-z²)/(1+z²)) ≅ 0.84·10^-4·Q² ,
where z=E′/E,
a₁=3·(1/4-5/9·sin²θ_W), a₂=3·(1/4-sin²θ_W),
G_F=1.166·10^-5 GeV^-2, sin²θ_W=0.236

The figure of merit is FoM ≅ A²·N_events. The figure of merit dependence on the scattering angle is presented on the next plot.

The figure of merit curve flattens out at small angles because of lower Q² and lower asymmetry. For W²>6 GeV² one should select θ>24°.

DIS kinematics
On this picture, the useful area is located between the lines X_Bj>0.55 and W²>4 GeV². The latter cut effectively limits the range to X_Bj<0.75 The lower cut θ>22° removes the high-rate background at small angles. The upper cut is chosen at θ<35°, taking into account the lower FoM at large angles and the features of the SoLID. For a different spectrometer (a dipole-based one, for example), one may consider larger angles.

Rates

For optimizing the SoLID performance, we consider the following kinematic range:

E_beam = 11 GeV
X_Bj>0.55
W²>4 GeV²
22°<θ<35°

It follows:

2.3<E′<6 GeV
6<Q²<12 GeV²

At the luminosity of 540 pb^-1s^-1 the full DIS rate in the given kinematical range:

0.55<X_Bj<0.75: ≅35.0 kHz with average asymmetry ⟨A⟩≅0.00071
0.65<X_Bj<0.75: ≅ 9.3 kHz with average asymmetry ⟨A⟩≅0.00078

Let us assume that the spectrometer's acceptance is 100%, while the total efficiency (beam delivery, DAQ, event reconstruction etc.) is 50%. Then, in order to obtain a 1% statistical accuracy one needs:

0.55<X_Bj<0.75: ≅20·10⁹ events, 13 days
0.65<X_Bj<0.75: ≅16·10⁹ events, 40 days

SoLID

Solenoid

The simulations have been done for a the BaBar solenoid, described in a NIM paper. Please note that there is likely a typo in Table 4, namely the "cryostat Inner diameter" of 1420 mm probably means the radius, not the diameter.

It is assumed that we can get the BaBar coil with the cryostat. Using the BaBar yoke is problematic - the solenoid axis would be about 50 cm above the beam in Hall A. This yoke is build from steel plates, interleaved with detectors. A more compact yoke can be built.

The field calculations were done using POISSON, with the regular currents in the coil, as used in BaBar:

Coils parameters
Coil R1, cm R2, cm Z1, cm Z2, cm Full current, A

1 152 154 -86.4 86.4 1706400

2 152 154 -172.8 -86.4 1706400

3 152 154 86.4 172.8 1706400

**Coils parameters**
Coil	R1, cm	R2, cm	Z1, cm	Z2, cm	Full current, A
1	152	154	-86.4	86.4	1706400
2	152	154	-172.8	-86.4	1706400
3	152	154	86.4	172.8	1706400

In order to provide a 1.5 T field at the solenoid center one should provide both a barrel and endcap yokes. The frontal endcap should also shield off the magnetic field down to a few Gs level, in order to be used with the polarized ³He target. The rear endcap should provide enough space for the detectors, positioned outside of the bore.

Poisson calculated field map

Magnetic field on Z-axis

The details on these calculation are given here.

PVDIS design

Beam and Target

We are planning to use:

50 μA, 11 GeV beam
2×2 mm² fast raster
40 cm liquid hydrogen of liquid deuterium target

The full luminosity on hydrogen would be L≅540 pb^-1s^-1

Basic Geometry

I used the coil fiducial volume of R_inner=137.5 cm (from Fig.1) and Z_length=385.0 cm (from Table 4). The coil center is located at the center of the Lab frame. The target center is tentatively located at the frame center as well. This provides an angular coverage of θ<35.5°.

The tentative layout of the setup includes an electromagnetic calorimeter, a gas Cherenkov detector and coordinate detectors, located on the rear sides of several wheels. These wheels may play a role of collimators, or baffles, selecting secondary particles in a certain kinematic range.

Momentum resolution

It occurs that a reasonable momentum resolution can be obtained just with the detectors at the exit of the coil area. There is no real need to position the detectors close to the target. The radial projection of the useful trajectories are nearly straight and provide a good enough position reconstruction of the track origin in the target. Using the existing beamline equipment and models, the rastered beam X-Y coordinates are predicted with a a precision of <0.5 mm for every event. In order to estimate the momentum resolution of the setup, an empirical method was used. DIS electrons in the range of interest were simulated and traced through the setup using GEANT3, with all physical processes turned off, apart from the energy loss. Only the detectors 6 and 8 were used. They were split radially in 1-2 cm intervals. For each combination of intervals r₆-r₈, the momentum was extrapolated using a linear formula p = α_° + α₁·1/Δφ(8-6) + α₂·r₆ + α₃·r₈ and scattering angle was approximated using: θ = β_° + β₁·ΔR(8-6) + β₂·Δφ(8-6) where the parameters α,β were fit to the simulated data. The model was accurate enough to provide in the absence of multiple scattering and detector smearing a momentum resolution of 0.1% and an angular resolution of 0.1 mrad. . The next figure shows the obtained energy resolution for data simulated with the multiple scattering and detector resolution included. With a reasonable detector resolution of about 0.5mm, the momentum resolution is about 2.5% while the angular resolution is about 1 mrad. The resolution of Q² is about 2.5%, while the X_Bj resolution is 0.025. The momentum is shifted on average by 2% due to the radiation losses in the material. The φ resolution is about 3 mrad.

Resolutions

Residuals

Residual in phi

Rates

The solenoid provides a momentum cutoff of about 0.3 GeV. The rates of particles hitting the calorimeter (on hydrogen):

DIS total for X_Bj>0.1: 2.5 MHz
DIS for X_Bj>0.55, W²>4 GeV² Q²>6 GeV² : 34 kHz
DIS for X_Bj>0.65, W²>4 GeV² Q²>6 GeV² : 8.5 kHz
π^- for P>0.2 GeV/c : 2300 MHz, with average energy deposit in the calorimeter of 0.27 GeV
π^- for P>1.0 GeV/c : 460 MHz
π^- for E_CALORIM>2.0 GeV : 320 kHz

The trigger will be based on the energy deposit in the calorimeter. In order to select the DIS events in the region of interest, the threshold depends on the radius of the calorimeter module (in cm): E_CALORIM>E_thresh(R), E_thresh(R)≅3.2 GeV/(R-20)*130-0.1 .

π^- for E_π> E_thresh(R): 890 kHz
π^- for E_CALORIM> E_thresh(R): <27 kHz

The low energy background from electromagnetic processes was estimated using GEANT3 with the standard energy cut of 1 MeV for photons and electrons. Such calculations have been compared with measurements in Hall A. The calorimeter response happens to be accurate within about 30%, while the wire chamber rate is underestimated by GEANT3 by a factor of 3-5.

The rates in the coordinate detectors are shown in the next plot. The dashed lines correspond to the "baffled" geometry. The calculated rates in the chambers 4-5 are about 25 kHz/mm², the real rates may reach 100 kHz/mm². The GEM detectors have been used at 30 kHz/mm² (COMPASS).

The energy flux in the calorimeter is shown on the next plot. At small angles the flux of 10⁷ GeV/module/sec would deposit about 1 GeV of energy in the typical ADC gate window of 100 ns.

Since the BG rates in the detectors seem to be too high, a system of baffles is considered.

Optimization of the baffles

A high rate of photons coming from the target, as well as a high low momentum pion flux would limit the operations of the spectrometer discussed. A relatively narrow momentum spectrum of the particles of interest allows us to implement a system of baffles which would filter out both strongly bending low momentum particles and straight photons. Several disk-shaped absorbers can be inserted downstream of the target. These disks should have sets of relatively narrow slits, which form channels, shaped in order to let the useful particles produced in a certain azimuthal range Δφ to pass through. The goal is to provide an overall acceptance of 30-50% of the full azimuthal coverage of 2π, for the scattered electrons in the selected range. One should try to maximize the value of Δφ in order to simplify the geometry and reduce the effects of slit scattering.

In the reference frame used the axis Z looked along the beam. The solenoid magnetic field turned electrons toward larger values of the azimuthal angle φ. The field map calculated for the SIDIS configuration was used. After several iterations an approximate φ range was defined, as Δφ(θ)=5°+4°·(θ-22°)/(35°-22°). In total, 8 absorber disks (or wheels) were considered, located at the following Z-positions (in cm):

 30.  60.  90. 120. 150. 180. 280. 300.

The distance of 1 m between the #6 and #7 is reserved for a gas Cherenkov detector. The wheel #8 is redundant and probably not needed.
The following procedure was applied (see this page for technical details):

For the 1-st iteration of the slits' sizes and locations a GEANT geometry was defined. Instead of the baffles a set of thin cylindrical detectors were inserted. Initial slit contours were calculated, for one channel only. For that, single electrons were simulated, produced at 20 polar angles θ_i from 22 to 35°. At each θ_i the minimum and the maximum electron energy were calculated, for 0.6<X_Bj<0.8 and W²>4 GeV². The maximum momentum particles, produced at the given θ_i and φ=180°-Δφ/2 were used to define the lower φ contours of the slits. The minimum momentum particles, produced at the given θ_i and φ=180°+Δφ/2 were used to define the upper φ contours of the slits. For each p,θ,φ-point 1000 tracks were simulated, which origin uniformly populated the taget length. The beam spot was 0.2×0.2 mm² size, no rastering was included at this moment. Using these data, the contours of the slits were defined as functions φ(r), approximated by 4 second order polinomials.
A kumac used the slit definitions obtained at step 1) to print out the FFREAD commands for the baffles and detectors geometry definitions, to be used by GEANT. This kumac can use additional cuts on the slits (see step 3)). The step of the slit structure (the number of channels) is defined at this stage. Tentatively, the minimal reasonable step of ΔΦ=12° was taken, which would make 30 channels. Later, the step will be optimized by simulating various physical backgrounds.
Using the previously obtained baffles geometry I ran GEANT, with DIS produced in the range of interest, making the baffles media a dead absorber, with GEANT physics set to zero, except for LOSS. This gives the spot size of the particles detected, in each detector. The same was done with straight tracks (by turning the magnetic field to zero), in order to check whether prompt photons would reach the detectors. After additional cuts on the slits have been defined in order to obscure the line of sight for the slit 6 (in front of the gas Cherenkov detector), step 2) was repeated.
At the end of the previous iterative procedure the geometry of the baffles was finalized. The results for the step ΔΦ=12° are shown below. The same KUIP macros provide the input geometry files for COMGEANT for the further MC simulation. A baffle ring is made of lead 9 cm thick. The input geometry files are located here.

The baffles reduce the BG rates in the coordinate detectors by a factor of 10-100 (see this plot), to a level below 15 kHz/mm² (taking into account a scaling factor of 5 from GEANT3 to the Hall A measurements). The energy flux in the calorimeter (see this plot) is reduced by a factor of 100.

Rates

The baffles leave about 36% of the useful rate and reduce the background rates by factors 10-100:

DIS total for X_Bj>0.1: 100 kHz
DIS for 0.55<X_Bj>0.75, W²>4 GeV² Q²>6 GeV² : 12 kHz
DIS for 0.65<X_Bj>0.75, W²>4 GeV² Q²>6 GeV² : 3.1 kHz (120 days to get 1% stat accuracy at 50% efficiency)
π^- for P>0.2 GeV/c : 140 MHz, with average energy deposit in the calorimeter of 0.13 GeV
π^- for P>1.0 GeV/c : 70 MHz
π^- for E_CALORIM>2.0 GeV : 80 kHz
π^- for E_π> E_thresh(R): 290 kHz
π^- for E_CALORIM> E_thresh(R): <10 kHz

Detectors

Overview

The following detectors have been used in the simulation:

GEM coordinate detectors downstream of the wheels 4-8. A GEM detector covers a ring with radii defined by DIS at 22°<θ<35°. One detector is 1 cm thick and amounts to 0.7% of radiation length. No stripe structure is considered at the moment. GEM detectors are high rate-capable coordinate detectors, proven to work at a particle flux of >30 kHz/mm².
ECAL - electromagnetic calorimeter, located in front of the read yoke plate. It can by built of a SPACAL-type (or SHASHLYK-type) lead-scintillator material with RL=1.32 cm. It contains a preshower detector 8 cm thick followed by a shower detector 22 cm thick. Without the baffles, the low-energy radiation dose in 4 months of operation will be about 200 krad, while with the baffles, it is reduced to 2 krad. The latter is within the lead glass capabilities.
Gas Cherenkov threshold detector GCH at the exit of the bore. It is about 1 m long, filled with C₄F₁₀. The refractive index is 1.41 at 300 nm and the pion threshold is 2.64 GeV/c. The gas choice is a matter of further optimization, however C₄F₁₀ is very popular for low thresholds (and high light yields) as well as for a very good transparency down to 160 nm. The typical borosilicate window PMTs spectral response was used for the photodetector. A spherical mirror was used, with reflectivity similar to one used in Hall B, about 3% RL thick. While the baffle structure included 30 sectors, GCH was split into 15 sectors, each covering 2 baffle sectors. Each GCH sector had a mirror and one or two photodetectors. It turns out that the mirror reflects light from 2 baffle sectors to 2 separate spots on the photodetector plane, allowing to use one independent detector for each baffle sector. Thin non-transparent screens separated the adjacent GCH sectors. The input/output windows were 0.2/0.5 mm thick.

The layout of the setup is shown on the following figure. A few DIS events simulated are displayed, including showering in the calorimeter and tracing of the Cherenkov light. For this case the baffles were built of an ideal absorber.

The next figure shows 20 DIS events simulated in the region of interest, with baffles made of lead. The showers are mostly absorbed before the 4-th wheel.

The next figure shows 50 π^--production events simulated in a region p>1 GeV/c, 18°<θ<36° using the Bosted-Wiseman fit. The red trajectories display charged particles, the dotted blue ones display photons, the black dash-dotted ones - neutrons and green dashed ones - muons. More than 4 wheels are needed to absorb pions.

Detector response and event selection

Detector response to electrons scattered in the range of interest, as well as to pions and various backgrounds have been simulated.

The ECAL resolution was assumed to be better than σE/E ≅ 0.1·E^-0.5. The calorimeter should be segmented in radius in order to apply higher thresholds at lower radii. The full (preshower plus shower) response to charged pions is presented on the following plot (left). The ECAL deposit is lower than the particle energy, which helps to suppress pions in the trigger since the pion spectrum is softer than the electron spectrum of interest. Another leverage against pions is given by lower relative response of the preshower in comparison with the full energy (see the right plot).
The GCH focusing with the large (2 sectors covering) spherical mirror is perhaps not the optimal. The photon spot on the photodetector plane is presented at the next plot, separately for 2 sectors (blue and red). The spots are nearly completely separated. One can provide 2 mirrors, either increasing the separation, or combining the spot on one photodetector. For the first try I use 2 separate photodetectors, assuming the separation is complete. In order to reduce the background from low energy electrons the photodetectors should be as small as reasonable. The size used is indicated with the black ellipse on the plot.

A problem with the focusing is illustrated on the next plot. The number of photoelectrons does not depend on the scattering angle for the large detector (left plot), while it drops with the angle for the small detector (right plot). One may hope to improve it by using two mirrors, or a different mirror shape.
With the current optics the mean number of photoelectrons for DIS detection is about 24 with the large detector and about 18 with the small one (see the left and right plots on the next figure). For the small detector about 90% of events have N_pe>10.

DIS secondary electrons were simulated in the kinematic region of interest, as well as pions and straight tracks. Also, minimum bias events were simulated.

Trigger

The trigger can be based on the calorimeter signal. The threshold depends on the radius of the hit (discussed above): E_CALORIM>E_thresh(R).

DIS total for X_Bj>0.1: 35 kHz
DIS for 0.55<X_Bj>0.75, W²>4 GeV² Q²>6 GeV² : 12 kHz
π^- : < 10 kHz

Other Options for the Spectrometer

I also tried a different setup, base on 2 BNL dipoles (gaps 46x120x120cm³). With these 2 dipoles centered at +/-30° (no baffles), the acceptance is about 50% of the solenoid with the baffles. At 40° one may hope to avoid baffles in the dipoles. At 40 deg the acceptance is about 18% of the full area 35<θ<45°. The figure of merit is lower at 40° than at 30°. One needs 180 days for 1% at X>0.55 and 500 days for 1% at X>0.65. These values were obtained with a 2 T field. A 1 T field does not increase the acceptance significantly (10% or so).

E-Mail : gen@jlab.org
Last updated: Feb 2, 2007