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Stato dei lavori. Ottimizzazione dei wiggler di DA F NE. Simona Bettoni. Outline. Method to reduce the integrated octupole in the wiggler of DA F NE Analysis tools at disposal: Multipolar analysis: I n (also vs x shift at the entrance)

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Stato dei lavori

Stato dei lavori

Ottimizzazione dei wiggler di DAFNE

Simona Bettoni


Outline

  • Method to reduce the integrated octupole in the wiggler of DAFNE

  • Analysis tools at disposal:

    • Multipolar analysis: In (also vs x shift at the entrance)

    • Tracking: x (y) and x’ (y’) vs x (y) shift at the entrance (tools Tosca+Matlab)

  • Shifted poles & cut poles models

  • Axis optimization

  • Analysis of the results:

    • Multipolar analysis

    • Tracking

    • Comparison with the experimental data at disposal

  • In the future


Other methods to reduce the integrated octupole
Other methods to reduce the integrated octupole

CURVED POLE

Reduction of the octupole around the beam trajectory in the region of the poles

Proposed by Pantaleo

MOVING MAGNETIC AXIS

Compensation of the integrated octupole in each semiperiod

New method


Multipolar expansion of the field with respect to the beam trajectory
Multipolar expansion of the field with respect to the beam trajectory

  • Determination of the beam trajectory starting from the measured data

  • Fit of By between -3 cm and +3 cm by a 4º order polynomial in x centered in xT(z) = xT

xT+3 cm

Beam trajectory (xT)

xT-3 cm


The integrated multipoles in periodic magnets
The integrated multipoles in periodic magnets trajectory

In a displaced system of reference:

y

y’

xT

bAk → defined in the reference centered in OA (wiggler axis)

bTk → defined in the reference centered inOT (beam trajectory)

O T

OA

x

x’

Even multipoles →

Left-right symmetry of the magnet

Multipoles change sign from a pole to the next one

Sum from a pole to the next one

Odd multipoles →


Method to reduce the integrated octupole displacement of the magnetic field
Method to reduce the integrated octupole: trajectorydisplacement of the magnetic field

WITHOUT POLE MODIFICATION

In each semiperiod the particle trajectory is always on one side with respect the magnetic axis

Octupole

WITH THE POLE MODIFICATION

Opportunely choosing the B axis is in principle possible to make zero the integrated octupole in each semiperiod

In each semiperiod the particle travels on both sides with respect to the magnetic axis


Optimization of the pole of the wiggler
Optimization of the pole of the wiggler trajectory

  • Goals

  • Reduce as less as possible the magnetic field in the gap

  • Maintain the left-right symmetry

FC1-like

FC2-like

FC 1

FC 2


Analysis trajectory

For each z fit of By vs x in the system of reference perpendicular to the beam trajectory


Cut poles model: analysis perpendicular to s trajectory

IFC = 693 A

I3 calculated over the entire wiggler varies of more than a factor 2 if the analysis is performed perpendicular to s and not to z!


Sector poles wiggler trajectory

IFC = 693 A

Cut the poles in z to have sector poles

I3 calculated over the entire wiggler perpendicular to z is 9.09 T/m3 with respect to 4.13 T/m3 of the analysis perpendicular to z


Shifted poles solution trajectory

$ and field roll-off


Shifted poles model trajectory

For the moment shifted the coils with the poles


Cut-shifted poles: the comparison of the field (at the same current = 550 A in FC)

CUT POLES

SHIFTED POLES


Cut-shifted poles: the comparison of the field (at the same current = 550 A in FC)

With the shifted poles solution, the field roll-off is improved, therefore the shims can be eliminated maintaining more or less the same dependence of the solution on the x-shift at the entrance.

Shim thick in cut poles solution = 1.15 mm x 2 = 2.3 mm/37 mm = 6 % gap

By(z = 0, x = 0)SHIFTED POLES = By(z = 0, x = 0)CUT POLES+7.6%


Trajectory optimization current = 550 A in FC)

Determined the best value of the current in HC to minimize the integral of By over z


Trajectory optimization current = 550 A in FC)

By integrated over z = 2 G.m

  • Exit angle = 8 x 10-2 mrad

  • x-shift exit-entrance = 0.13 mm


Tools analysis: multipoles with Tosca & Matlab current = 550 A in FC)

  • TOSCA

  • Determination of the best beam trajectory (tracking Tosca)

  • For each z found By in the points on a line of ±3 cm around (xTR, 0, zTR,) and perpendicular to the trajectory

  • Fit of the By at each point of the line (Tosca) at steps of 1 mm (fit Matlab)

  • MATLAB

  • Determination of the best beam trajectory (tracking Tosca/0 the integral of By over z)

  • For each found z points on a line of ±3 cm around (xTR, 0, zTR,) and perpendicular to the trajectory

  • Fit of the By at each point of the line at steps of 1 mm interpolated by Matlab


Tools analysis: tracking current = 550 A in FC)

  • Beam enters at several x

  • Tosca tracks the trajectory of each beam

  • Calculated the x exit-xTR NOM and x’exit in function of the x-shift at the entrance

The curves are only to show the tool


Axis optimization current = 550 A in FC)

For the moment used these codes to optimize the position of the axis


Multipoles current = 550 A in FC)

Presence of spikes in my analysis


Multipoles current = 550 A in FC)

Beam trajectory at fixed Dz and parabolic interpolation in z


Spikes current = 550 A in FC)

Spikes: solved problem


Axis optimization current = 550 A in FC)

0.73 cm

Minimized I3 calculated in the entire wiggler


Multipolar analysis: to summarize current = 550 A in FC)

To do the first optimization I used this technique


Analysis of the results: tracking (±3 cm) current = 550 A in FC)

Beam enters from x = xTR NOM-3 cm to x = xTR NOM+3 cm at steps of 1 mm, where xTR NOM is the position of entrance of the nominal trajectory


Analysis of the results: tracking: the x exit (±3 cm) current = 550 A in FC)

The fit is satisfactory already for the 3rth-4rth order

Coefficient of the 3rd order term = 13 m-2


Analysis of the results: tracking: the x’ exit (±3 cm) current = 550 A in FC)

Coefficient of the 3rd order term = 10 rad/m3

The fit is satisfactory for the 3th-4th order


Analysis of the results: comparison with the experimental data

I could compare the results only with the results of the experimental map at about 700 A

Ho riscalato curva di Miro x_exit = x_exitMIRO-x_exitMIRO(xENTR = 0)


Analysis of the results: comparison with the experimental data

I could compare the results only with the results of the experimental map at about 700 A




Conclusions data

  • Shifted poles - cut poles solution comparison:

    • The field roll-off is improved  no shim  increased BPEAK

    • Cheaper

  • At present:

    • improved the linearity zone of x and x’ with respect to the field map at dipsosal

  • In the future:

    • Shifted poles solution analysis:

      • Analysis of the field maps by Dragt, Mitchell and Venturini (the map considered the best one by us, one with the poles more centered and one with the poles more shifted)

    • Measurement of the field map of the wiggler at I = 550 A to have a real comparison with the results of the simulation (at LNF, at ENEA?)



Situation in the present configuration (I = 693 A): x exit data

The fit is satisfactory for the 5rth-6rth order

│Coefficient of the 3rd order term │ >200 m-2


Situation in the present configuration (I = 693 A): x’ exit

│Coefficient of the 3rd order term │ ~600 rad/m3

The fit is satisfactory for the 6rth order


Trajectory optimization exit

To determine the best value of I in HC for the several axis displacements


Fine! exit


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