MAD parameters 9/8/2004

Updated 10/13/04 for typos. Changes are blue.

MAD parameters 9/23/2004

Normal*[]**	m	radians		m-ster.	m-rad		cm	%	Half-envelope (cm)[†]
angle	drift	Δθ	Δφ	ΔΩ=πΔθΔφ [‡]	σθ	σφ	σy	σδ	x	y
12°	7	0.073	0.025	5.7	0.9	0.5	0.7	0.09	83	35
20°	3.2	0.131	0.0335	13.8	1.7	0.5	0.4	0.13	94	33
35°	1.65	0.19	0.038	22.7	2.5	0.5	0.3	0.16	105	30
Septum 5°
Full gap	7	0.073	0.020	4.6	0.9	0.5	0.7	0.09	83	35
Reduced gap		0.05	0.020	3.1	0.9	0.5	0.7	0.09	79	35
Quads off		0.0383	0.0381	4.6	0.4	0.5	0.9	0.17[§]	85	75 [**]
Just Dipoles [††]
12°	7	0.0375	0.0405	4.8	0.4	0.5	0.9	0.2§	84	74**
12°	7	0.0375	0.019	2.2	0.4	0.5	0.9	0.2§	84	35
35°	1.65	0.0578	0.0623	11.3	0.4	0.5	0.7	0.15§	91	83**
35°	1.65	0.0578	0.026	4.7	0.4	0.5	0.7	0.15§	91	35
Peculiar Tunes
Reversed quads I	7	0.032	0.059	5.9	0.1	0.1	0.9	0.02	39	105**
Reversed quads II	7	0.025	0.073	5.7	0.1	1.6	~0	0.10§	77	72**
MAD + Q₂	7	0.065	0.039	8.0	0.3	0.5	0.7	0.02	39	71[‡‡]

Notes:

Please read the footnotes.
Acceptance determined from TRANSPORT (y₀ = ±1 cm, δ = ±15%).
Angular and position resolutions based on 1^st order TRANSPORT assuming 100 micron position and 0.5 milli-radian angular resolutions. Except where noted, momentum resolution (σδ) based on worst case (δ = 15%) correction from x|θδ (same position and angular resolution assumptions)
Bend angle is 30° (10° + 20°)[§§]
Nominal Central momentum is 7.5 GeV/c
Re higher P₀: below are tabulated the fields need for 8 GeV/c (it’s nice to have a margin when you design a magnet). The “no quad” tunes in principle will be workable at higher P₀, but it will depend on the details of the magnet design. Paul Brindza estimates that just turning off the quadrupole component will get you 10 to 20% more dipole (20% is really stretching things). A good idea, suggested by Paul, is to build the magnets with leads such that 2 of the quadrupole coil sectors could have their polarity reversed making the quadrupole coil pack an auxiliary dipole pack. Then it will depend on the details (peak fields etc.), but just 30% more would take 8 GeV/c to 10.4 GeV/c. Add 15% to that and you’ve got 11.96 GeV/c!

Magnet parameters for 8 GeV/c

Dipoles	∫Bdl (T-m)
Magnet 1	4.66
Magnet 2	9.31

Quadrupoles:			∫Bdl (T-m) at r = 60 cm
“Normal”	12°	1^st MAD Quad	4.79
	12°	2^nd MAD Quad	-4.22
	20°	1^st MAD Quad	6.64
	20°	2^nd MAD Quad	-4.95
	35°	1^st MAD Quad	8.59
	35°	2^nd MAD Quad	-5.51
Septum	5°	1^st MAD Quad	4.76
Septum	5°	2^nd MAD Quad	-4.20
Reverse Quads I	12°	1^st MAD Quad	-2.80
Reverse Quads I	12°	2^nd MAD Quad	5.10
Reverse Quads II	12°	1^st MAD Quad	-5.40
Reverse Quads II	12°	2^nd MAD Quad	9.79
MAD + Q₂	12°	1^st MAD Quad	-4.37
		2^nd MAD Quad	5.08
		Q₂	1.955[***]

[*] Normal tune means 3.9 m behind the 2^nd magnet (x|θ) = 0 and (y|y0) = 1 (This is not the same as some previously reported “normal” tunes.)

[†] half-envelope dimensions from TRANSPORT 3.9 m behind 2^nd magnet

[‡] The “elliptical” assumption used here might be a slight underestimate.

[§] Here there is no momentum focus so the 1^st order limit (x|θ * σ_θ)

[††] Quadrupoles turned completely off will allow a higher P0 (maybe 10-20% higher?)

[‡‡] Here maybe we could turn the detector on its side or go for more momentum acceptance and less horizontal acceptance.

[§§] Reducing the bend angle could be used to go to higher central momentum

[***] At r = 30 cm. This is actually harder than you can push this magnet. At 1600 amps you get 1.5718 T-m. Reducing this magnet reduces the vertical acceptance, but only slowly.