# PEP II

## High Energy Ring ### PEP II for electrons (HER)

A High Energy Ring was designed using Win-AGILE, a tool by P. J. Bryant for lattice design on Windows. Check the repo.

#### Data used:

• 192 Dipoles
• Circunference: 2200 m
• Electron energy: 8.973 GeV
• Size of standard cell: 15.2 m

#### Calculations

We first make an estimation of the total number of cells in the ring:

``2200 / 15.2 = 144.7 cells``

Next, we calculate the number of elements per cell:

``(192 D + 290 Q) / 144.7 = 3.33 elements per cell``

The Dipole / Quadrupole ratio is approximately `1.5`. Since the number of elements per cell is not an integer, instead of taking one cell as a unit, we take 3 cells of `15.2 m`, where we can fit in 4 Dipoles and 6 Quadrupoles. The number of "triple" cells we have is `48`.

``````48 x 4 = 192 D
48 x 6 = 288 Q``````

We still need to fit in 2 Quadrupoles. We have 47 identical cells and one where we will put the 2 Quadrupoles. Then we make an estimation of the size of each element, taking the proportions used previously as reference:

``Quadrupoles = 1    Dipoles = 5    Drifts = 10``

and we obtain the following values:

``Q = 0.31 m    D = 1.8 m    Dr = 3.52 m``

Now, we calculate the deflection angle:

``θ = 2π / 192 = 0.032725 rad``

To calculate the `k-quad` constant we check the distance between Quadrupoles:

``d = 3.88 m``

Since the condition of stability is `f ≥ d / 2`:

``f ≥ 1.94 m``

and

``f = 1 / kL``

then,

``k < 1 / fL, with L = Rθ``

and we obtain:

``k = 0.045``

#### Simulations with Win-AGILE

The values obtained from these calculations were introduced in the Win-AGILE simulator using two files:

• PEP I, with 48 identical units, in compressed format
• PEP II, with 47 identical units and one different, in decompressed format

Since PEP II was not working, PEP I (all units identical) was used. Some values were changed, like the size of the elements of the lattice, based on the specifications of the real PEP, and the value of `k` for the track to be correct.

Based on these modifications, the data was recalculated:

``````Q = 0.56 m    D = 3.80 m    Dr = 2.60 m
θ = 2π / 192 = 0.032725 rad

d = 3.16 m
f ≥ d / 2    ⇒    f ≥ 1.94 m
k < 1 / fL, with L = Rθ

k = 0.0055`````` Check the repo. Share on Twitter or follow me! Published: 2004-05-09 23:43

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