B2 correction algorithms for TCHROM

The current supplied to the sextupoles will be the sum of a term to set the desired chromaticity, and a term to compensate for the time dependent drift of b₂ on the 150 GEV porches. The sextupole current responsible for compensation of the time dependent drifts will be loaded into the 465 cards called C:SFB2 and C:SDB2.

I_SF = x +-3.31*(150/1000)*< b₂> è I_SFb2 = -.4965*<b₂>

I_SD = x = -5.1*(150/1000)*< b₂> è I_SDb2 = -.765*<b₂>

On both the Front Porch and Back Porch, b₂ has the functional form:

eq. 1) b₂ = b_2i + (m * ln(t + c))

where t is the time spent on the 150 GEV porch.

On the back porch, the terms in equation 1) are calculated as follows:

b_2i = .082 * ln(T_FT)

m = -.196 - (.024 * ln(T_FT))

c = 20 sec

where T_FT is the number of seconds spent on the previous flattop. The values .082, -.196, .024, and 20 will eventually be constants supplied to TCHROM by a CRG library routine.

On the front porch, the terms in equation 1) are calculated as follows:

b_2i = -.04 * ln(T_BP/60) - [(.161 - (.0277 * ln(T_BP /60))) * ln(T_FT)]

m = .342 - .0208*[2*ln(T_BP) - ln(T_FT)]

c = 0

where T_FT is the number of seconds spent on the previous flattop, and T_BP is the number of seconds spent on the previous back porch. The values .04, .161, .0277, .342, .0208 and 0 will eventually be constants supplied to TCHROM by a CRG library routine.

For now, on event $42, the current should be linearly removed from SFB2 and SDB2 over 5 seconds. This will eventually be a slightly more complex time table.

When coming into the back porch, the current is SFB2 and SDB2 must gracefully approach b_2i. There still needs to be an algorithm to ramp the current up to b_2i on the back porch.

The snap back that occurs at start of ramp (event $42) will be a time table that begins where the front porch H-table is just before the ramp. The only parameter that will be an input to the time table calculation will be the duration of the time table (T). The time table itself will be a polynomial of the form:

b₂ = b_2i + at² + ct⁴

b_2i = b₂ at the time the ramp is loaded,

which is the final value of b2 on the front porch.

c = b_2i /T⁴

a = -2cT²

The deceleration ramp may need a time table that starts at zero and ends up at b₂ at the start of the back porch. The reason for this ramp is to smoothly connect the back porch table with the deceleration ramp. This ramp would need to be triggered by event $6D and the final value for the ramp would be b₂ (t=0) for the back porch H-table (this is not b_2i on the back porch - we will call this value b_2f). The only parameter that will be an input to the time table calculation will be the ramp length (T).

In order to calculate the table, the OAC will have to know the length of the deceleration ramp (T:BPSTRT). The time ramp should be all zeros until time = (T:BPSTRT - T) (we will call this time T₀). From time t = T₀ until t = T:BPSTRT the time table will be calculated as follows:

b₂ = T^-2(t-T₀)² b_2f

This diagram describes the times involved in this calculation. $6D is defined to occur at time 0.

Test mode loading of the sextupoles can be done by setting a value to T:CHRCOM. Setting this device will force a download of the B2 devices as if the proper state change had taken place. The values to load specific ramps are:
1 ->load front porch curve, 2 -> load unwind (snap back) curve, 3 -> load back porch match curve, 4 -> load back porch curve, 5 -> clear load status

Link to a block Diagram of the TCHROM OAC

Link to diagram of Camac Card configuration.