## Error studies for field maps

### Error studies for field maps

Dear Didier,

I wanted to perform misalignment studies with a solenoid field map. I looked at available error study commands and could not find the one that I can use with a field map. Also when I use a solenoid field map, do I need to set the parameters for statistic error->Magnet element in the Errors setup of the errors page of TraceWin.

Thank you

With Regards

Abhishek Pathak

I wanted to perform misalignment studies with a solenoid field map. I looked at available error study commands and could not find the one that I can use with a field map. Also when I use a solenoid field map, do I need to set the parameters for statistic error->Magnet element in the Errors setup of the errors page of TraceWin.

Thank you

With Regards

Abhishek Pathak

### Re: Error studies for field maps

Dear Abhishek,

All commands usable for QUAD, including setting or setting errors, are also applied to magnetic field maps

Regards,

Didier

All commands usable for QUAD, including setting or setting errors, are also applied to magnetic field maps

Regards,

Didier

### Re: Error studies for field maps

Dear Didier,

Thank you very much for your reply. I just have another small query.

Following the TraceWin manual, I am using the following command to study the effect of solenoid field map rotation about the z-axis,

ERROR_QUAD_NCPL_STAT N 0 0 0 0 0 0.0573 0 0 0 0 0 0 1

Here I consider

r=0-> The errors are constant and equal to each value of the command line.

dx=dy= φx(°)= φy(°) =dG(%)= dz(mm)= dG3(%)= dG4(%)= dG5(%)= dG6(%)=0

Nb=1-> I am considering only one solenoid.

φz(°)=0.0573 -> I am giving the rotation about z axis in degree.

May you please clarify what

Thank you

With Regards

Abhishek Pathak

Thank you very much for your reply. I just have another small query.

Following the TraceWin manual, I am using the following command to study the effect of solenoid field map rotation about the z-axis,

ERROR_QUAD_NCPL_STAT N 0 0 0 0 0 0.0573 0 0 0 0 0 0 1

Here I consider

r=0-> The errors are constant and equal to each value of the command line.

dx=dy= φx(°)= φy(°) =dG(%)= dz(mm)= dG3(%)= dG4(%)= dG5(%)= dG6(%)=0

Nb=1-> I am considering only one solenoid.

φz(°)=0.0573 -> I am giving the rotation about z axis in degree.

May you please clarify what

**indicates?***"N"*Thank you

With Regards

Abhishek Pathak

### Re: Error studies for field maps

Dear Abhishek,

The N parameter defines the number of elements following the ERROR command that will be affected by these errors. If in this sequence of elements a new command is present, it cancels the previous command from its position to redefine the errors for the next N elements.

I realise that this information is indeed missing in the manual, I will clarify this point

Regards,

Didier

The N parameter defines the number of elements following the ERROR command that will be affected by these errors. If in this sequence of elements a new command is present, it cancels the previous command from its position to redefine the errors for the next N elements.

I realise that this information is indeed missing in the manual, I will clarify this point

Regards,

Didier

### Re: Error studies for field maps

Dear Didier,

Thank you very much.

With Regards

Abhishek Pathak

Thank you very much.

With Regards

Abhishek Pathak

### Re: Error studies for field maps

Dear Didier,

While using the command,

if I chose r=2 for Gaussian distribution, what is the cutoff value for the distribution that the code takes (is it three times RMS or six times RMS)? I wanted to know this to have an estimate of the maximum error used in the simulations.

Thank you

With Regards

Abhishek Pathak

While using the command,

ERROR_QUAD_NCPL_STAT N r(0/1/2/4/5), dx(mm), dy(mm), φx(°), φy(°), φz(°), dG(%), dz(mm) , dG3(%), dG4(%), dG5(%), dG6(%), Nb

if I chose r=2 for Gaussian distribution, what is the cutoff value for the distribution that the code takes (is it three times RMS or six times RMS)? I wanted to know this to have an estimate of the maximum error used in the simulations.

Thank you

With Regards

Abhishek Pathak

### Re: Error studies for field maps

Dear Abhishek Pathak,

There is no cutoff.

Regards,

Didier

There is no cutoff.

Regards,

Didier

### Re: Error studies for field maps

Dear Didier,

Does it mean that the error can be arbitrarily large following the infinite tail of the Gaussian distribution? Is there a way to define a cutoff?

Thank you

With Regards

Abhishek Pathak

Does it mean that the error can be arbitrarily large following the infinite tail of the Gaussian distribution? Is there a way to define a cutoff?

Thank you

With Regards

Abhishek Pathak

### Re: Error studies for field maps

Dear Abhishek Pathak,

Yes I confirm this point.

In addition, the impact of the errors on the statistical rms values of the beam (rms size, emittance, centroid...) are dominated by the rms value of the errors whatever the chosen error distribution.

Now, if you are interested in rare events such as the loss of one or more particles, even with billions of different runs, there is statistically no chance that an error will be larger than 5 rms

That said, it's not too difficult to add a cutoff value if you think it would be really useful, but I'm convinced that unless you choose 2 or 3 rms, you wouldn't see any difference beyond 4 rms.

Regards,

Didier

Yes I confirm this point.

In addition, the impact of the errors on the statistical rms values of the beam (rms size, emittance, centroid...) are dominated by the rms value of the errors whatever the chosen error distribution.

Now, if you are interested in rare events such as the loss of one or more particles, even with billions of different runs, there is statistically no chance that an error will be larger than 5 rms

That said, it's not too difficult to add a cutoff value if you think it would be really useful, but I'm convinced that unless you choose 2 or 3 rms, you wouldn't see any difference beyond 4 rms.

Regards,

Didier

### Re: Error studies for field maps

Dear Didier,

Thank you very much for the explanation. I was concerned because I observed significant particle loss for my lattice and was wondering if it is because of the large deviation from the rms misalignment that I have chosen to perform my error studies. In certain cases, we would like to keep the maximum deviation within 3 sigmas and look at the emittance growth and beam transmission. In such cases having an option to choose a cut-off can be useful.

Thank you

With Regards

Abhishek

Thank you very much for the explanation. I was concerned because I observed significant particle loss for my lattice and was wondering if it is because of the large deviation from the rms misalignment that I have chosen to perform my error studies. In certain cases, we would like to keep the maximum deviation within 3 sigmas and look at the emittance growth and beam transmission. In such cases having an option to choose a cut-off can be useful.

Thank you

With Regards

Abhishek