Fitting the Fully Coupled ORM for the Fermilab Booster

The orbit response matrix (ORM) method [1] is applied to model the Fermilab Booster with parameters such as the BPM gains and rolls, and parameters in the lattice model, including the gradient errors and magnets rolls. We found that the gradients and rolls of the adjacent combined-function magnets were deeply correlated, preventing full determination of the model parameters. Suitable constraints of the parameters were introduced to guarantee an unique, equivalent solution. Simulations show that such solution preserves proper combinations of the adjacent parameters. The result shows that the gradient errors of combined-function magnets are within design limits.