Design of active-target TPC

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

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 .

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.

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

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)

Electric field

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

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

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

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

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

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

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.

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

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

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

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

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

Electric field Without shield wire Shield wire : 5mm pitch

Electric field Shield wire : 2.5mm pitch

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

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)

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.

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

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

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

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

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

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

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

Condition Energy loss of recoil nuclei : 500 electrons/cm proton 30MeV @Ar(70%)+CO2(30%) : 700 electrons/cm a with 15MeV/u @He(90%)+CO2(10%) : 500 electrons/cm Transverse diffusion （RMS） Transverse diffusion coefficient of He(90%)+CO2(10%) : 200mm for 1cm(RMS) 200mm 400mm 600mm 1000mm

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

Diffusion Other than the border of 2 pads → Almost same z 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.

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

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°

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

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

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)