The main purpose is to measure the Parity Violation effects in DIS (PVDIS) at XBj>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. The azimuthal acceptance is about 30%. A way to increase the acceptance is to use toroidal magnets. This is the topic of this document.
The figure of merit is FoM ≅ A²·Nevents. The figure of merit dependence on the scattering angle is presented on the next plot.
At the luminosity of 540 pb-1s-1 the full DIS rate
in the given kinematical range:
An optimized optics using ideal toroids with constant fields is shown on the next picture.
The baffles at small angles shade the detectors from the target. The fields are:
TOR1 needs a uniform field of 2.5 T at R=0.4-1.5 m. This requires
I=5 MA at R=0.4 m and I=18.75 MA at R=1.5 m,
changing linearly with R. For comparison, the G0 magnet provides a full current current of
I=5.76 MA at R≅0.5-1.5 m.
The SC cable which can be used was assumed to be a 20x5 mm² copper bar containing 36 "strands".
Each strand is a round wire 0.6 mm diameter, consisting of 36% of superconductor and 64% of copper.
For the starting point, the G0 toroidal magnet was simulated.
The coil sizes are taking from the appropriate drawings, with a few mm accuracy.
The coil consists of 36 turns per layer, with 4 layers.
Calculated field map for G0, 8 coils (1) at Z=0, at I=5kA per wire (turn).
The field of the G0 toroid is much lower than 2.3 T, needed to focus the DIS electrons
in the range of interest.
The TOR1 coil consists of 49 turns per layer, with 4 layers.
Calculated field map for 8 coils (1) at Z=0, at I=10kA per wire (turn).
Calculated field map for 12 coils (2) at Z=0, at I=6.66kA per wire (turn).
A more realistic coil would have rounder windings. Also the coil is made longer
in order to reduce the current.
This coil consists of 47 turns per layer. 8 coils with 6 layers/coil (type 12) can produce
the needed field at 6.66 kA.
Calculated field map for 8 coils (type 12, 6 layers/coil) at Z=0, at I=6.66kA per wire (turn).
The maximum field in the coil is 6 T.
Calculated field map for 16 coils (type 11, 4 layers/coil) at Z=0, at I=5.00kA per wire (turn).
16 coils may provide a match for the 8-coil G0 magnet.
The maximum field in the coil is 4 T. It might be possible to use only 2 layers/coil at 10 kA.
Detected sample, θ-φ-dependence, for the field maps (1) and (2). For TOR2
the ideal toroid was taken, without any absorption in the coils.
Close to the coils, at the lower radii of R<100 cm, the field has a radial component.
This component cases a "defocusing" of the trajectories at smaller scattering angles,
moving them toward the coil. At larger angles some focusing occurs, with the trajectories
moved to the center of the sector.
The effect is illustrated on the next picture for the map (2), made with no absorption
in the ideal TOR2 coils. The effect leads to a loss of acceptance, since some of the
"defocused" electrons hit the coil of TOR2.
The trajectories for DIS at φ=12°, 22°<θ<35°, 0.65;<x<0.85. The field map (1) was used.
Detected sample, θ-φ-dependence, for the field map (1), with 8 sectors. For the TOR2
a scaled copy of TOR1 was taken, with thinner coils (11 cm instead of 15 cm). The right plot
demonstrate the effect of the sectors matching.
Detected sample, θ-φ-dependence, for the field map (2), with 12 sectors. For the TOR2
a scaled copy of TOR1 was taken, with thinner coils (11 cm instead of 15 cm).
The next figure
shows the obtained energy resolution for data simulated with the physics processes included
and with the ideal detector resolution.
The next two figures
shows the obtained energy resolution for data simulated with the physics processes included
and with the detector resolution of 0.2mm and 0.4mm. In this range, the resolutions are dominated by
the multiple scattering and the energy loss, rather than by the detector resolution.
A different magnet configuration simulated included 8-coils TOR1 and TOR2. For TOR1 the field map 1 was used,
the field scaled up by a factor 1.1. For TOR2 the G0 field map was used.
The field integral of the G0 magnet is smaller than the integral of TOR2 from the previous configuration.
Still, the resolutions are only slightly worse than in the previous case (see the next figure).
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°.
On this picture, the useful area is located between the lines XBj>0.55 and
W²>4 GeV². The latter cut effectively limits the range to XBj<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/DDS. For a different
spectrometer (a dipole-based one, for example), one may consider larger angles.
Rates
For optimizing the spectrometer performance, we consider the following kinematic range:
It follows:
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:
DTS
Concept
With a toroidal spectrometer, the tracking detectors can be positioned
in a shade from the target view, downstream of the magnet. However,
with long targets, the momentum can not be measured. Therefore, we are considering
two toroidal magnets:
Both TOR1 and TOR2 bend electrons toward the beam.
The detectors are located between TOR1 and TOR2 and downstream of TOR2, all in the shade
from the target. The fields are defined by:
The azimuthal acceptance can can be as large as 90%, while all types of backgrounds
are expected to be much lower than in the SoLID design. Drawbacks are
the need to build new magnets, the limitation to particles with one charge
(a solenoid without baffles can take both), potentially larger error on the scattering angle,
and, possibly, others.
Ideal Optics
I found that a regular B∝1/R field toroid does not focus well the particles
of interest. I am considering a toroid with a constant field, with the current, crossing
a circle of radius R, being I∝R. A coil is filled uniformly with
the wire.
Toroids
The average azimuthal (along φ) field at a radius R is
Bφ=μoI⁄(2πR)=2·10-7I⁄R,
where R is the current flowing through the circle of radius R. The units are T, m, A.
Parameter
G0
TOR1
Ideal
Calculation 1
Calculation 2
Number of coils
8
8
8
12
Full current along Z at R=0.4 m
5.76 MA
5.00 MA
5.00 MA
5.00 MA
Full current along Z at R=1.5 m
5.76 MA
18.75 MA
18.75 MA
18.75 MA
Superconductor cable
20 strands
36 strands
36 strands
36 strands
Cross section of the copper support cable
20×5 mm²
same
same
same
Current density
5000 A/cm²
10000 A/cm²
10000 A/cm²
6666 A/cm²
Cable layers per coil
4
2
4
4
Coil cross section, at R=0.4 m
8×18 cm²
4×15.6 cm²
8×8 cm²
8×8 cm²
Full coil thickness in φ
15 cm
11 cm
15 cm
15 cm
Bφ at ≅0.4 m
2.88 T
2.50 T
2.30 T
2.30 T
Bφ at 1.5 m
0.77 T
2.50 T
1.43 T
1.64 T
Bmax
-
-
7.6 T
5.5 T
Full current density dI/dR at R=0.4-1.5 m
none
125 kA/cm
125 kA/cm ?
125 kA/cm ?
Cables per unit length in R, at R=0.4-1.5 m
none
0.78 per cm
1.25 per cm
1.25 per cm
Coil cross section, at Rmax≅1.5 m
8×18 cm²
4×60 cm²
8×30 cm²
8×30 cm²
Full number of turs per coil
-
-
196
196
Stored energy, MJ
7.6
-
52
45
Acceptance
Effects caused by the field non-unoformity
The azimuthal field on the central radial line of the sector drops with the radius,
which causes a drop of efficiency for large θ angles at the sector center.
This drop is relatively smaller for the 12-coils TOR1(2).
Coils of TOR2
It was assumed that TOR2 has the same geometry as TOR1 and the same field map,
scaled down by a factor 0.4. No serious optimization of the scaling factor
has been done so far. Because of the lower field the coil thickness was reduced from 15 to 11 cm
(2 layers instead of 4, plus the cryostat).
Results
The acceptance was calculated in a range of:
It was required, that the scattered electron hits the 1-st detector of the 1-st arm (between the TOR1 and TOR2
magnets), as well as the calorimeter (the last detector of the 2-nd arm, downstream or TOR2) .
For the triggering and DAQ
purposes it would be simpler to keep all the sectors of the spectrometer
independent on each other. Therefore, the particle should cross the same sectors in both arms.
Configuration
Acceptance
TOR2 - no absorption
TOR2 - regular
Sectors match
8 coils, map (1)
0.53
0.39
0.31
12 coils, map (2)
0.51
0.34
0.31
Kinematical resolutions
In order to estimate the kinematical resolutions of the setup, as the momentum, the
scattering angle as well as Q² and XBj resolutions,
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. Since the magnetic field is not really axially symmetric,
only particles produced in the central plane of one sector were simulated. For other azimuthal
angles, a more complex procedure has to be applied. The straight parts of the trajectory
(T1 between two magnets and T2 downstream of the second magnet) are reconstructed
assuming the ideal detector resolution. The coordinates of the T1 intersections
with the central planes of two magnets are calculated: R1=T1(Z=ZTOR1) and
R2=T2(Z=ZTOR2). Both R1 and R2 were split in 1-cm intervals and
in each interval the simulated data were approximated by a linear combination of certain variables ( θ1 and θ2
denote the trajectory angles in the radial plane):
The model was accurate enough to provide a momentum resolution of 0.04% and an angular resolution
of 0.5 mrad
in the absence of multiple scattering and detector smearing, which is illustrated by the next figure.
The 12-coils TOR1 and TOR2 were used, both providing the field map 2, but the TOR2 field was reduced by a factor 0.4.
Configuration
TOR1
TOR2
Acceptance
Resolutions
σX,Y=0.0 mm
σX,Y=0.2 mm
σX,Y=0.5 mm
coils
map
scale
coils
map
scale
regular
sector
match σP/P
% σθ
mrad σQ²/Q²
% σXBj
σP/P
% σθ
mrad σQ²/Q²
% σXBj
σP/P
% σθ
mrad σQ²/Q²
% σXBj
2
12
2
1.0
12
2
0.4
0.34
0.31
0.71
2.95
0.87
0.0041
0.74
3.10
0.90
0.0042
3
8
1
1.0
8
G0
1.0
0.39
0.31
1.00
4.20
1.11
0.0050
1.05
4.48
1.12
0.0052
1.13
5.83
1.14
0.0058
E-Mail :
gen@jlab.org
Last updated: Apr 1, 2008