Field cage capacitance, stored energy and spark down behavior

To find Ca and Cb

The length of the outer field cage stripe

Conductor pitch

Outer Conductor width

Inside or buried conductor width

Conductor overlap width

kapton thickness

Gas insulator thickness

Dielectric constant of kapton

permittivity of air

Capacitance for two kapton sheets

Find gap voltages

Field cage voltage

Maximum stripe number

Evaluate the recurrsion relations

Initial condition

from equation 6

Initial condition

The total charge that can go into the spark is the sum of charges on the
internal capacitiors, Ca, and the external capacitors Cb. This will happen
if the highest potential ring shorts to ground and a spark zippers along
all the rings.

total charge on all the internal capacitors

total charge on all the external capacitors

test voltage required to
generate the same charge
that is stored on half of
the field cage

Total stored energy on the outer skin of outer field cage:

stored energy on the internal
capacitors

stored energy on external
capacitors

Test voltage required on the test capacitor to duplicate
half of the stored field cage energy

Treating as a lumped system, without proper
starting condition.

Now that we have two skins the total stored energy of the full cage ignoring
the inner field cage is (He-Ethane operation):

For P10 operation

Calculation of time constants:

internal stripe to stripe time constant

this is an overestimate of the time constant since this assumes all the capacitance to ground has the full