Algorithms for emittance evaluation

Emittance measurements

Slit-grid devices

•Trusted method•Wire current resolution 1pA•Integration time 1us..Nsec•Spatial resolution ~100um•Measurement time minutes

Slit-grid control software

Pepper-pot measurements without scintillating screen

Use of optical registration

An example of optimal resolution ratio for single shot operation

Dedicated algorithms and outputs

Scattering effects in screens, holes and slits

Pepper-pot calibration

Pinhole effective radius calibration Estimation of the light scattering

effect in the screen Pinholes zero position calibration

with low-emittance light beam

Use of multiple profile monitors

Use of variable quadrupole strengths

Longitudinal emittance measurements

Timo Milosic. Thursday. 10:50

Ellipses and linear optics

Canonical distributions

Universal algorithms

Mostly exist for two-dimensional phase space

Applicable for any measurement type

•Data transformation: applying of linear optics element, resampling etc.•Noise and fraction reduction•Data healing tools•2-D emittance calculation

Use of KV-plane for the emittance estimation

Use of statistical momentums

Use of optimal fitting methods

Use of parametric data fit

A comparison of different methods

Errors estimation

Noise added to the data value Errors due to the model simplification Limitation of the parameterized model Limited accuracy of parameters of

involved beam optics elements Non-ideal registration equipment (non-

linearity, aberrations, cross talk,… )

Typical output of the emittance evaluation results

Typical preliminary data evaluation in 2-D space

An example of an interactive tool for 2-D emittance evaluation

Few nice output plots which good to have for report and publications

-For standalone applications – OpenGL primitives library- To save some time one may use TeeChart- Tools based on MATLAB or MathCAD could be easily adapted to any new ideas. License cost is critical.

Typical preliminary data evaluatin in 2-D space

A data manipulation possibilities are always demanded

The basic evaluation uses only first order integration algorithms

Main calculations in EmitView are executed on the data matrix. Each element of this matrix owned an elementary current. In the assumption that the current density is uniformly distributed on the surface of elementary cell, this current is equal to product Ii,k=Ji,k*dx*dy. Where J is the current density in the phase space coordinates. Thresholds and KV levels are defined as a percentage of the maximum elementary current value.Captured current and KV plane are defined as a part of full current, which is sum of all elementary currents.

RMS emittance for defined KV level is calculated by formula.Statistical parameters for given formula are calculated for current density weighted elementary cells. Only cells with current higher then KV level are taking into account.

Pepper pot algorithms

- Image processing technique

- Limited spatial resolution

- 4- dimensional phase space

Pepper-pot ‘classical’ data preparation

EMITTANCE MEASUREMENTS AT THE NEW UNILAC PRE-STRIPPER USING A PEPPER-POT WITH A PC-CONTROLLED CCD-CAMERA. M.Dolinska et al. DIPAC 1999, Chester. UK.

Noise cancellation

Local spot filtering

Parametric nonlinear data fitting

Image evaluation cycle

Horizontal profile

An example of a heavy ion beam investigation

7kV 10kV 14kV

Beam divergence as a function of applied potential

An example of a heavy ion beam investigation(2)

An example of a heavy ion beam investigation(3)

An example of a heavy ion beam investigation(4)

Parametric nonlinear data fitting