1. Design of active-target TPC

2. Contents Physics requirements Basic structure Gas property
Position difference
Distortion of electric field by ions created by beam
Around GEM
Pad shape

3. Physics requirements Study for nuclear property of unstable nuclei
→ Use of inverse kinematics is needed.
Measurement of forward scattering
→ Measuring the recoil light nuclei can lead to precise measurement.
→ But the energy of the recoil nuclei for forward scattering is very small.
→ Gaseous target (or thin foil) is needed.
Gas
Target : a → He gas
Target : d → d gas (or Cd4)
To separate the objective reaction from other reaction,
Angler resolution : 7.45mrad(RMS)
Position resolution of vertex point : 1mm(RMS)
Energy resolution : 10%(RMS)
is needed for .

4. Basic structure Mask the beam track area
It is difficult to measure the track of beam(Z: 10-50) and the track of recoil nuclei(Z: 1 or 2) at the same detector.
(Energy loss of beam is several hundreds times larger than that of recoil nuclei.)
→ TPC can be operate in high rate beam condition.
(Only the rate of recoil nuclei has to be taken into account.)
Use of GEM
Electron multiplication can be done at high rate.
Pad shape(rectangular triangle)
To lessen the number of pads, rectangular triangle is used for the pad shape.
Position is derived by the charge ratio of the neighboring two pads.

5. Schematic view 1 Beam Recoil nuclei 10cm ☓10cm Thickness : 100mm
Field cage
GEM
10cm ☓10cm
Thickness : 100mm
Pad
Total volume :
565mm ☓ 668mm ☓ 520mm

6. Schematic view 2 4cm NaI (CsI) Wire (pitch: 2.5mm) GEM Field cage
Recoil nuclei
Beam
4cm
25cm
Beam
GEM
Mesh
GEM
Recoil nuclei
Pad
NaI (CsI)

7. Electric field

8. Gas property He(90%) + CO2(10%) (760 Torr, 300 K) Drift velocity
Townsend coefficient

9. He(90%) + CO2(10%) (760 Torr, 300 K)
Longitudinal diffusion
Transverse diffusion

10. Ar(70%) + CO2(30%) (760 Torr, 300 K)
Drift velocity
Townsend coefficient

11. Ar(70%) + CO2(30%) (760 Torr, 300 K)
Longitudinal diffusion
Transverse diffusion

12. D2(100%) (760 Torr, 300 K)
Drift velocity
Townsend coefficient

13. D2(100%) (760 Torr, 300 K)
Longitudinal diffusion
Transverse diffusion

14. Distortion of electric field
If the beam rate is very high, beam comes before the ions created by previous beam go away.
→ Ions (electrons) created by beam are piled up, and distorts the electric field.
After a few seconds, charge distribution will be stationary.
← This Charge distribution is simulated by Monte-Carlo simulation.
Distortion of the electric field is simulated by Garfield,
← Put stationary charge distribution into Garfield’s configuration, substitute wire for electric charge.
and simulation of the position gap during electron drift has done.

15. Condition for simulation
Gas property
Gas: He(90%) + CO2(10%)
Electric field : 1kV/cm
Pressure : 760 Torr
Temperature : 300 K
Drift velocity : 3 [cm/ms]
Ion mobility : 2.5☓103[cm2·Torr·V-1·s-1]
Beam
Beam rate : 107 Hz
Energy loss : 4 MeV/cm = 105 ions(electrons)/cm
← corresponds to Sn with 100MeV/u
Beam spread :
5cm (RMS) for drift direction
1cm (RMS) for the other direction

16. y
Charge distribution
Field cage
Field cage
Recoil nuclei
25cm
Beam
Generate random number (Gaussian; mean: 12.5cm, RMS: 5cm).
← corresponds to beam hit position, where ions(electrons) are created.
Add to the histogram.
GEM
Pad
Move each bin data to the next bin.
← corresponds to time change, the move of ions(electrons).
count
count y y
repeat

17. Distribution of ion Ion distribution for each 1[ms] stationary
Take the average of these histogram

18. Distribution of electron
Electron distribution for each 1[ms]
stationary
Take the average of these histogram

19. Position difference Put electrons at
x : every 5mm from x=2.5cm to x=13.0cm
y : 24.0cm
Drift electrons to the end of field cage, and subtract the point where electron is put from end point.
→ Position difference < 0.745mm.
The effect of diffusion is not considered
Simulate position difference in 3 different shield wire configuration.
Without shield wire
5mm pitch
2.5mm pitch y
Field cage
Field cage
y=24cm x
2cm
13cm
Shield wire

20. Electric field
Without shield wire
Shield wire : 5mm pitch

21. Electric field
Shield wire : 2.5mm pitch

22. Result 1 Active area of GEM is 2.5cm < x < 12.5cm
Without shield wire
Shield wire : 5mm pitch
Without shield wire
Maximum position difference is over 1mm
Shield wire : 5mm pitch
Maximum position difference : ~ 0.745mm

23. Result 2 Active area of GEM is 2.5cm < x < 12.5cm
Shield wire : 2.5mm pitch
Shield wire : 2.5mm pitch;
Without ions & electrons
Shield wire pitch : 2.5mm
Maximum position difference is within 0.3mm < 0.745mm
→ Change of track angle is less within 3mrad.(flight length: 10cm)

24. Position gap between mesh to pad
GEM
Pad
Frame of GEM
0.6
0.25
0.19 ~ 0.20
0.14 x
-1.3
1.3
-15.4
-12.7
-2.3
2.3
12.7
15.4
Put electrons at
x : every 1mm (-13.5cm<x<-11.5cm & -3.5cm<x<-1.5cm)
y :
Between mesh and GEM
→ 0.59cm(0.01cm below Mesh)
Between GEM(or frame) and pad
→ 0.18cm(-12.6cm<x<-11.5cm or -3.5cm<x<-2.4cm; 0.01cm below GEM)
or 0.13cm(other area; 0.01cm below frame)
Drift electrons from mesh to GEM & from GEM(frame) to pad, and derive the position difference.

25. Result (Mesh-GEM) -13.5 < x < -11.5 -3.5 < x < -1.5
Frame width : 10mm
Active area of
GEM
-13.5 < x < -11.5
-3.5 < x < -1.5
Overlap with GEM & frame : 1mm
Overlap with GEM & frame : 0.5mm
Overlap with GEM & frame : 0mm

26. Result (GEM-Pad) -13.5 < x < -11.5 -3.5 < x < -1.5
Frame width : 10mm
Active area of
GEM
-13.5 < x < -11.5
-3.5 < x < -1.5
Overlap with GEM &
frame : 1mm
Overlap with GEM &
Frame : 0.5mm
Overlap with GEM &
Frame : 0mm

27. Result (Mesh-GEM) -13.5 < x < -11.5 -3.5 < x < -1.5
Overlap with GEM & frame : 0mm
Active area of
GEM
-13.5 < x < -11.5
-3.5 < x < -1.5
Frame width : 5mm
Frame width : 10mm
Frame width : 15mm

28. Result (GEM-Pad) -13.5 < x < -11.5 -3.5 < x < -1.5
Overlap with GEM & frame : 0mm
Active area of
GEM
-13.5 < x < -11.5
-3.5 < x < -1.5
Frame width : 5mm
Frame width : 10mm
Frame width : 15mm

29. Pad shape Pad shape : rectangular triangle (16mm☓16mm)
Position is derived by the charge ratio of the neighboring two pads.
Angler resolution < 7.45mrad(RMS)
Hit position is fitted by line using the least squares method.
16mm

30. Derivation of position 1
Recoil nuclei Q1
z = Q2 / (Q1 + Q2) ☓ 16mm
x = Q2 / (Q1 + Q2) ☓ 16mm x z Q2
Recoil nuclei Q2 Q1 x
z = Q1 / (Q1 + Q2) ☓ 16mm
x = Q1 / (Q1 + Q2) ☓ 16mm z Q2
Derive wrong position!
→ Thinking about the algorism to derive correct position in such case Q1 x
Recoil nuclei z

31. Derivation of position 2
Recoil nuclei x Q1 Q2
For these cases, position is derived by the same way. z
Recoil nuclei Q1 x z Q2

32. Condition Energy loss of recoil nuclei : 500 electrons/cm
proton : 700 electrons/cm
a with : 500 electrons/cm
Transverse diffusion （RMS）
Transverse diffusion coefficient of He(90%)+CO2(10%) :
200mm for 1cm(RMS)
200mm
400mm
600mm
1000mm

33. Simulation Arrival position of electron x : z :q
16mm
Simulation x
16mm
Arrival position of electron
x :
z :
Ru : uniform random number between -1 and flight length+1
Rdx : Gaussian random number, which corresponds to diffusion length for x direction
Rdz : Gaussian random number, which corresponds to diffusion length for y direction
: incident angle
z0 : incident position
Number of generated random number : n±√n n=500[electrons/cm]×(flight length+2)
Number of events : 10000 z

34. Diffusion Other than the border of 2 pads → Almost samez
Diffusion
: 200mm
: 400mm
: 600mm
: 1000mm
z : injection position for z
Other than the border of 2 pads → Almost same
Border of 2 pads → Better angular resolution for the smaller diffusion.

35. Pad size 16mm×16mm : most good angular resolution
z : injection position for z
16mm×16mm : most good angular resolution

36. Oblique incidence (angular resolution)
Diffusion : 1000mm
Better angular resolution can be achieved in the case of q<0 than in the case of q>0.
q = -15°
q = -30°

37. Oblique incidence (vertex resolution)
Diffusion : 1000mm
Vertex resolution is less than 1mm.
q = -15°
q = -30°

38. Summary & Outlook Final design is Wire pitch : 2.5mm Frame of GEM
Overlap of GEM & frame : 0mm
Frame width : 10mm
Pad size : 16mm × 16mm
→ Performance
Angular resolution : 4.5mrad
Position resolution of vertex point : 0.5mm
Position difference : < 0.3mm(Field cage) + 0.2mm(Mesh-Pad)
Outlook
Tracking algorism

39. Substitution wire
To consider the beam spread for x-axis, wires are put at x=1.
The voltage which supplied to substitution wire(V) is
V0 : electrical potential made by field wires
q : electric charge at unit length
lground : distance from wire to ground
lwire : diameter of wire y
Field cage
Field cage x
Substitution wire for electric charge (x=1)