1. What I’ve been doing

2. My Problem: Conceptually LHeC: linear electron collider Basic Design: linac will be connected to a recirculation track (why?) Goal: to determine a design for the linac + recirculation structure that will… --Optimize $$$ --Minimize radiative energy loss --Minimize emittance growth

3. Before getting started, let’s think of some possible designs “Race-track” Design **Single or Double Acceleration? **How many revolutions for optimum energy gain

4. My Design Proposal “Ballfield” Design **How many revolutions? **Reason: certainly reduce energy loss, and maybe even cost

5. My Problem: Analytically Energy Loss to Radiation:

6. Analytical (cont.) So an e - that passes angle θ in circular track of radius R, will experience radiation energy loss: In the Linac, it will experience an energy gain:

7. My Problem: Computationally (my algorithm) This optimization problem calls for 8 variables: 1. Injection energy 2. Target energy 3. Energy gradient (energy gain per meter in Linac) 4. No. of revolutions 5. bool: singly acc. structure corresponds to 0, while doubly acc. corresponds to 1 6. Cost of linac per meter 7. Cost of drift section per meter 8. Cost of bending track per meter

8. Algorithm (cont.) The whole goal is to minimize the cost function 2 variables: radius and length!! For single acceleration structure: Total Cost (R,L) = 2π R n $bend + L $drift + L $lin For double acceleration structure: Total Cost (R,L) = 2π R n $bend + 2L $lin Looking at our structure, and using the energy formulas from the previous slides, you can construct a function that gives the final energy value of the e- beam, E = E (Ei, R, L, dE, revs, bool) We now have the necessary restriction to our optimization problem: the final energy for the dimensions (R and L) must equal to the target energy.

9. The Parameters Used 1. Injection energy = 500MeV 2. Target energy = {20, 40, 60, 80, 100, 120} GeV 3. Energy gradient = 15 MeV/m 4. No. of revolutions: trials from 1 to 8 5. bool: trials with both 0, 1 6. Cost of linac per meter = $160k/m 7. Cost of drift section per meter = $15k/m 8. Cost of bending track per meter = $50k/m

10. Some Sample Results

13. Limitations Assumes a constant energy gradient Assumes cost of bending track independent of size of bend. In reality, the cost of a bending magnet increases with the dipole strength, k. k ∝ 1/R → smaller turns require larger magnets, and would increase the bending track cost. Implementing this concept into my algorithm will probably yield higher radii for optimal cost. Model does not yet consider lattice structure and the overall optics behind the design; however, the model targets the key parameter—cost—and gives very strong insight into the optimal structure. Model does not yet consider operating cost.

14. How I will improve model Introduce dummy parameter λ, which will have units of $M / GeV. The new function to be optimized will be: Total_Cost + λ × Energy_Loss This will allow us to consider “operating” cost to some extent, while limiting energy loss. Try new functions for the cost of bending track, such that cost decreases with increasing radius.

15. Coming Attractions My “Ballfield” design Emittance growth and lattice design

16. Questions?