====== BAM Group======

====== THAT'S RIGHT ======

====== B A M ======
===== DAY 1: =====

2. We are using the **St. George** recoil separator to study the reactions:
<sup>22</sup>Ne(α,γ)<sup>26</sup>Mg,

<sup>22</sup>Ne(α,n)<sup>25</sup>Mg

3.

b. The (x|x) term is the magnification of the x-position. The (x|a) term is the focusing factor for angle a. (a|a) is the magnification of the a angle. The (a|x) term is the focusing factor for position x. 

c. An increase in the energy leads to a decrease in the amount of bending due to the dipole magnet and vice versa. Here you can see two rays with +/- 5% change in energy.
{{ :dispersion.png?400 |}}
The blue ray has the increase in energy while the red ray has the decrease.

**Remember to take the transpose of the transport matrix given by COSY to extract matrix elements correctly.**

===== DAY 2: =====

4. For the (α,n) channel, the important beam energy in inverse kinematics is ~3.8 MeV beam of <sup>22</sup>Ne. The corresponding max recoil angle is ~35mrad, and the recoil energy spread is ~ 7.3%. A plot of the recoil 
angle and energy spread as a function of beam energy:
{{::ne-alpha-3.8mev-kinematics.png?400|}}
{{::angle-energy-acceptance.png?400|}}

This reaction is very difficult - it barely fits in St. George, and the predicted cross section is incredibly small for the neutron channel. The threshold for the neutron channel corresponds to a beam energy of 3.12 MeV.

5. The most recent measurement of the neutron channel is given in this paper: {{ ::the_key_neutron_source_in_massive_stars.pdf |Jaeger et al.}}

6. Modifying the emittance script to (file:{{ ::emittance_script_auto_loop.rar |}}), it loops through the Quad field tip strength around the minima and saves VMAX(RAY(1)) to a file. 

The provided slides define K as the inverse of the focal length of the 'thin lens'. For a quadrupole, K = 1/f = G*L_eff/(B*rho). After this conversion, plotting this data and fitting results in:

{{::vmax2-vs-k.png?400|}}

Model: P1*x^2 + P2*x + P3

P1 = 3.82e-04+/-2.03e-06 m^2

P2 = 6.05e-05+/-4.22e-07 m^3

P3 = 2.59e-06+/-5.20e-08 m^2

{{::p6_eqns.png?400|}}

This, with the length to the quad center L=6.08505m, leads to an emittance of e = 0.237 mm*mrad. This is fairly close to the defined rays, which have an emittance of e = 1mm*0.2mrad = 0.2 mm*mrad.
 --------------------

===== DAY 3: =====

7. We are using COSY file for St. George.

https://wikihost.nscl.msu.edu/JIOSS/doku.php?id=st._george_cosy_model 


**Run St. George with normal settings, find mass resolution of 59.26
**

To print mass resolution, use command 

WRITE 6 'Mres = '&S(MRES);


Now vary effective length of Q3 by factor 1.03:

- defined in {section 2} as MQ LQ3+DLQ3 Q3*QF RQ3;


Change to:

''MQ 1.03*(LQ3+DLQ3) Q3*QF RQ3;''

''MQ <length> <flux density at pole tip> <aperture>''


Also need to reduce drift lengths either side of quadrupole so that position of center of quadrupole does not change.

Change drift before Q3 definition from

''DL DL6-0.5*DLQ3;''

to 

''DL DL6-0.5*DLQ3-0.03*(LQ3+DLQ3)/2;''


Change drift after Q3 definition from

''DL DL7-0.5*DLQ3-0.5*DLQ4;''

to 

''DL DL7-0.5*DLQ3-0.5*DLQ4-.03*(LQ3+DLQ3)/2;''


**New mass resolution after making this change is 38.1**

-------------------------------------------------------------
Improved method for changing effective length of Q3:
-------------------------------------------------------------
Line 545, we have definition ''DLQ3 := 0.353 - LQ3''

(This is the difference between measured effective field length and defined effective field length, LQ3)

Now we just need to change the measured effective length by PMOD*0.353 where PMOD is a variable for % modification, e.g. PMOD = 1.03 

Definition of MQ already includes factor ''DLQ3: MQ LQ3+DLQ3 Q3*QF RQ3;''

as do the drifts before and after:''DL DL6-0.5*DLQ3;'' and ''DL DL7-0.5*DLQ3-0.5*DLQ4;''

-------------------------------------------------------------
Attempt to recover best mass resolution:
-------------------------------------------------------------
To do this we will try to fit the strength of Q3. Doing this calculation to 5th order, we are able to recover the initial mass resolution of 59 with a Q3 quad strength of .88 which is a 2% decrease in the quad strength.

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===== DAY 4: =====
Today we are working on problem 8. We are using the command ''SA <DX> <DY>'' to change the beam position. ''SA <DX> <DY>'' offsets the optics axis x by DX and y by DY. To 5th order, changing the x offset by .5 mm leads to a 5% change in the mass resolution. Any amount of change of the y offset leads to no change in the mass resolution. This is pretty weird...
We changed the beam size by changing the values of variables X and Y. Increasing X by .1 mm caused the mass resolution to decrease by 5%. Increasing Y by the same amount leads to no change in the mass resolution...

By adding 2 mm to the lengths of quad 3 and 4 and decreasing the drift lengths after them by 2 mm, we reach a 5% change in the mass resolution.
We can shift optical elements in the x-y plane by placing the SA command before and after the element you are shifting. For instance, if you want to shift a quadrupole in the positive y-direction by 5 mm, you would use the following command:

 ''SA 0 .005;''

 ''MQ LQ3+DLQ3 Q3*QF RQ3;''

 ''SA 0 -.005;''

We used this command to shift quadrupole 3 up by 5 mm which changed the mass resolution by 5%. Shifting the quadrupole by 0.5 mm in the x-direction changes the mass resolution by 5%.

We can use the TA command to rotate the quad about the x and y axes. This has the same syntax as SA.
Rotating about the x-axis by .05° changes the mass resolution by 5%. Rotating about the y-axis by .15° changes the mass resolution by 5%.

To determine how much roll is allowed before changing the mass resolution by 5%, we use the RA command which takes one angle and rotates about the z-axis. An angle 0f 2.3° is allowed.