Re: back of the envelope

[Eugene Chudakov <gen@jlab.org>]

Mark,

At small steps, the deviation is proportional to the square of the step size.

Let us assume that the trajectory has been measured up to
a certain point and a certain radius of curvature is reconstructed (say, R).
The next step (which length is d radially, d<<R ) is done in an area where 
the field does actually deviate from our map by (dB/B). Then, the
trajectory would deviate from the predicted one by (approx):
d**2/2/R*(dB/B).
For d=50mm, dB/B=0.01, R=1000mm the deviation is 0.012mm, which is
negligible (unless I made a mistake with these simple calculations).

It is interesting, what is your deviation at a 5cm step in radius.

Eugene

On Fri, 27 Feb 2009, Mark M. Ito wrote:

> Eugene,
>
> All of the tracks start with zero separation and at this level of 
> approximation, the separation is 1/2 cm per % of deviation of B field per 60 
> cm of track length or roughly 80 microns per % of B field deviation per cm of 
> track length (again for this particular configuration). So if we take a B 
> field deviation of 10^-4 uniformly and a track length of 50 cm, we get a 
> position error of 40 microns. This is small when added in quadrature with a 
> 150 to 200 micron position resolution and will be "smaller" still when 
> multiple scattering is considered. Again a uniform deviation is not what we 
> are worried about, but this is just to set the scale (as you originally and 
> aptly suggested). As you know, the problem is that the non-uniform 
> distortions in field are very difficult to calibrate away.
>
> -- Mark
>
> P. S. Went back to cc'ing the list again.
>
> Eugene Chudakov wrote:
>> The separation grows with the radius.
>> At the last 5 cm step the separation increased somehow.
>> What is this increase? I must be small (0.5mm?), but it is
>> hard to say from the plots.
>> 
>> Thanks,
>> Eugene
>> 
>> 
>> On Fri, 27 Feb 2009, Mark M. Ito wrote:
>> 
>>> Not sure I understand the question. The separation of 1 cm is mention is 
>>> just obtained by eye looking at the plot.
>>> 
>>> Eugene Chudakov wrote:
>>>> Hi Mark,
>>>> 
>>>> as far as I see these are X-Y plots (not r-phi).
>>>> I guess, the deviation between two tracking steps matters. The full 
>>>> deviation of the trajectory will be absorbed in the momentum
>>>> measurement. The bottom plot shows the range in X (close to R for this 
>>>> area) of 5cm, which is about the distance between CDC
>>>> super-layers and is about 1 step in tracking. What is the increment 
>>>> between
>>>> the curves' separations at this step?
>>>> 
>>>> Thanks,
>>>> Eugene
>>>> 
>>>> 
>>>> On Fri, 27 Feb 2009, Mark M. Ito wrote:
>>>> 
>>>>> Folks,
>>>>> 
>>>>> At last Monday?s tracking meeting Eugene suggested that someone make an 
>>>>> estimate of the position error caused by a mistake in the knowledge of 
>>>>> the magnetic field. Here is an example: http://tinyurl.com/btp8jx
>>>>> 
>>>>> -- Mark
>>>>> 
>>> 
>>> 
>
>