# A glance at TPC gas gains

I had some confusion about the gas gain in the TPC, so I've decided to document what I've seen...

One can write the gas gain as an exponential:
Gain = exp(α*V + β)

The inner and outer sectors have different α, β, and overall gains. For now, I will ignore β, such that the gain is relative to the gain at nominal voltage, which is 1170 V for the inner sectors and 1390 V for the outer sectors. I will focus on α:
Relative Gain = exp(α*ΔV)

Here is what I found for versions of α, in units of [per volt]:
• STARNote 247 (1996), p. 27 (used currently for determining effective anode voltage over padrows influenced by multiple anode channels)
αinner = 0.01305
αouter = 0.01026
• STARNote 395 (1999), p. 1:
αinner = 0.01226
αouter = 0.00934
• STARNote 263 (1996), p. 20; STARNote 412 (1999), p. 2; STAR TPC Readout NIM paper (2003), p. 680:
αinner = 0.01267
αouter = 0.00934
• StTpcdEdxCorrection, St_tss_tssparC, and St_tpcCorrectionC classes, along with the database table Calibrations_tpc / tpcGainCorrection (used currently for dE/dx):
αinner = 0.011480079 -2.88086e-06*ΔV -1.58229e-07*ΔV2
αouter = 0.0094702689 +6.30584e-06*ΔV -6.01231e-08*ΔV2 -2.15159e-10*ΔV3
Here are the four curves for the inner and outer α values and relative gains in red, blue, green, and black respectively versus ΔV, where ΔV = 0 is nominal voltage (note that the blue and green curves overlap for outer sectors as α is identical for them). The values of α are (generally) lower for use in dE/dx than from the various STARNotes, and subsequently the dependence of relative gain on voltage used by dE/dx is notably flatter. The differences grow substantially with decreasing operating voltage.

-Gene