• PMT's 37' ( S3 has 36' 7.25" )

• pi+ and e+ background removal
• aero generate light even for pi's of 1GeV or less
• use ToF of S1 and S3 for region where aerogel efficiency < ~100%
• signal aero but no gas => pi+/-
• signal aero and gas => e+/-

• pi and e separation
• p(min)=17 MeV/c for e+/-
• =4.8 GeV/c for pi+/-
• signal aero but no gas => pi+/-
• signal aero and gas => e+/-

150 photons
linear to 1.5% till 6000 photo electrons
~1.3 photoelectrons per MeV     above 17.5 MeV
E >~0.5 GeV      N p.e. >~500
~10 p.e. per channel for 1%
max of 2000 p.e.

For wire tension measurements
Tension = 4 * (wire material density) * ((wire length)**2) * ((fundamental frequency)**2)

For charge injection
   Q = C * E
   1fC = 1pF * 1mV

i(t) = ( Q / ( 2 * T * LN( b / a )) ) * ( 1 / ( 1 + ( t / T )))
T = ( a**2 * LN( b / a ) ) / ( 2 * (positive ion mobility) * V )
i(t) = Current output as a function of time
T = chamber time constant
Q = total charge in avalanche
Rise is limited by velocity of sturation of ion mobility and
broadening terms such as diffusion.
For FPP
2 * a = 1 mil = 25.4 um
2 * b = 1 cm = 1E4 um
T = 963 um**2 / ( 2 * (positive ion mobility) * V )
V = 1600 Volts
1 / (mobility) = ( ((percent of mixture) / (mobility of gas)) + ((percent of mixture) / (mobility of gas)) )
for Argon/Ethane (68/32)
T = 2 ns
Z = 358 ohms

Capacitance for cylindrical tube wire chamber ( straw tube )
C=(2*PI*(permittivity))/(LN(R2/R1))
where R1 is outer diameter of inner conductor
where R2 is inner diameter of outer conductor
where permittivity of vacuum is 8.854e-12 F/m
for FPP
R1=12.7E-6 meters
R2=5e-3 meters
which gives C=9.31 pF/m

Capacitance for a planar cathode wire chamber ( PWC )
C=((2*PI*permittivity)/((PI*l/s)-(LN(2*PI*a/s)))
where permittivity of vacuum is 8.854e-12 F/m
for VDC
a=12.7e-6 meters
s=4.23e-2 meters
l=1.27e-2 meters
which gives C=7.71 pF/m

Alcohol additions are to insure all ions are -OH with low eV potential
for ionization.  Also, radiationless transitions due to vibrational
modes ( collision ).

Positive ion mobility for Ar/Iso (50/50)
                                          1/u+ = 11500 V*s/m**2
                                    density = 2.25 g/l
with 1% methylal          1/u+ = 12250 V*s/m**2
with 4% methylal          1/u+ = 13000 V*s/m**2

For gain variations in a tube (TM-1434)(Fermilab Note)
Variation with wire diameter;
     log(Gain)=(a*(wire diameter))+b         where a and b are constants
     for example cited a 1% change in diameter gave a 5% change in gain
Variation with wire displacement;
     (Gain of displaced)/(Gain of Nominal)=a*((displacement)/(gap height))**b       
     b from 2.0 on up.  Square 7mm tube gave b=2.3
Variation with high voltage;
     log(Gain)=(a*(voltage))+b
     2.4 to 2.5 change for 100V change          1V~=0.9% change in gain
     G1/G2=(const)**(V1-V2))
Variation with pressure;
     ln(Gain)=(a*(ln(temperature)))+b               with a=6.7
     G1/G2=(T1/T2)**6.7
     for 1degC => 2.3% change in gain
Variation with pressure;
     ln(Gain)=(a*(ln(pressure)))+b
     G1/G2=(T1/T2)**(-7.7)
     1% change in pressure => 8% change in gain