1 Design of active-target TPC

Contents I.Physics requirements II.Basic structure III.Gas property IV.Electric field Distortion by ground Distortion of electric filed by ions created by beam V.Pad shape 2

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 :  → He gas Target : d → d gas (or Cd 4 )  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 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.

Beam Field cage Pad GEM Recoil nuclei 25cm 10cm ☓ 10cm Thickness : 100  m Total volume : 565mm ☓ 668mm ☓ 520mm Schematic view

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

7 Gas property (simulated by Garfield) He(90%) + CO 2 (10%) (760 Torr, 300 K) Drift velocityTownsend coefficient Longitudinal diffusionTransverse diffusion

8 D 2 (100%) (760 Torr, 300 K) Drift velocityTownsend coefficient Longitudinal diffusionTransverse diffusion

9 Distortion by ground  The effect of ground is checked for 3 configurations. pitch : 2.5mm; double wire pitch : 5mm; double wire pitch : 2.5mm; single wire  Put electrons at x : every 5mm from x=0.5cm to x=13.0cm(active area of GEM : 2.5<x<12.5) 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. Field cage y 0 x y=24cm 13cm

Result mm pitch; single 5mm pitch; double Active area of GEM 2.5mm pitch; double Active area of GEM Wire of field cage has to be double. Active area of GEM is 2.5cm < x < 12.5cm

11 Distortion of electric field by ions  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.

12 Condition for simulation  Gas property Gas: He(90%) + CO 2 (10%) Electric field : 1kV/cm Pressure : 760 Torr Temperature : 300 K  Drift velocity : 3 [cm/  s]  Ion mobility : 2.5 ☓ 10 3 [cm 2 ·Torr·V -1 ·s -1 ]  Beam Beam rate : 10 7 Hz Energy loss : 4 MeV/cm = 10 5 ions(electrons)/cm ← corresponds to Sn with 100MeV/u Beam spread : 5cm (RMS) for drift direction 1cm (RMS) for the other direction

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

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

15 Field cage y 0 x  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=24cm Position difference 2cm13cm Shield wire

16 Result Without shield wire Shield wire : 5mm pitch Active area of GEM Active area of GEM is 2.5cm < x < 12.5cm Active area of GEM Without shield wire : Maximum position difference is over 1mm Shield wire : 5mm pitch : Maximum position difference : ~ 0.745mm Shield wire pitch : 2.5mm : Maximum position difference is 0.3mm < 0.745mm → Change of track angle is less within 3mrad.(flight length: 10cm) Shield wire : 2.5mm pitch Active area of GEM

17 Pad shape 16mm 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.

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

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

20 Condition  Energy loss of recoil nuclei : 500 electrons/cm proton : 700 electrons/cm  with : 500 electrons/cm  Transverse diffusion （ RMS ） Transverse diffusion coefficient of He(90%)+CO2(10%) : 200  m for 1cm(RMS) 200  m 400  m 600  m 1000  m

21 Simulation  Arrival position of electron x : z : R u : uniform random number between -1 and flight length+1 R dx : Gaussian random number, which corresponds to diffusion length for x direction R dz : Gaussian random number, which corresponds to diffusion length for y direction  : incident angle z 0 : incident position  Number of generated random number : n±√n n=500[electrons/cm]×(flight length+2)  Number of events : mm  z x

22 Diffusion : 200  m : 400  m : 600  m : 1000  m Diffusion Other than the border of 2 pads → Almost same Border of 2 pads → Tracking algorism is not good. 0 z z : injection position for z

23 Pad size : 8mm×50mm : 16mm×50mm : 16mm×25mm : 16mm×16mm : 20mm×20mm Pad size z : injection position for z 16mm×16mm : best angular resolution Diffusion : 1000  m

24 Inclined incidence 16mm  z x  In the case of inclined incidence, angular resolution and position resolution of vertex point are simulated.   : -30°, -15°, 0°, 15°, 30°  Pad size : 16mm × 16mm  Number of generated random number : n±√n n=500[electrons/cm]×(flight length+2)  Number of events : 10000

25 Result (angular resolution)  = 30°  = 15°  = 0°  = -15°  = -30° Diffusion : 1000  m Better angular resolution can be achieved in the case of  0.

26 Result (vertex resolution)  = 30°  = 15°  = 0°  = -15°  = -30° Diffusion : 1000  m Vertex resolution is less than 1mm.

27 Summary & Outlook  Final design is Wire pitch : 2.5mm (double) Pad size : 16mm × 16mm → Performance Angular resolution : < 4.5mrad Position resolution of vertex point : 0.5mm Position difference : < 0.3mm  Outlook Tracking algorism Include the effect of straggling

28 Backup

29 Field cage y 0 x Substitution wire for electric charge (x=1)  To consider the beam spread for x-axis, wires are put at x=1.  The voltage which supplied to substitution wire(V) is V 0 : electrical potential made by field wires q : electric charge at unit length l ground : distance from wire to ground l wire : diameter of wire Substitution wire

30 Ar(70%) + CO 2 (30%) (760 Torr, 300 K) Drift velocityTownsend coefficient

31 Ar(70%) + CO 2 (30%) (760 Torr, 300 K) Longitudinal diffusionTransverse diffusion

Electric field(distorted) 32 Without shield wire Shield wire : 5mm pitch

33 Electric field(distorted) Shield wire : 2.5mm pitch

34 Position difference between mesh to pad ~ x 0.14 GEM Pad Frame of GEM  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.

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

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

37 Active area of GEM -3.5 < x < < x < Result (Mesh-GEM) Frame width : 5mmFrame width : 10mmFrame width : 15mm Overlap with GEM & frame : 0mm

38 Active area of GEM -3.5 < x < < x < Result (GEM-Pad) Frame width : 5mmFrame width : 10mmFrame width : 15mm Overlap with GEM & frame : 0mm