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Merged
merged 8 commits into from
Sep 11, 2023
Merged

Backtracking Improvements #404

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04dbe10
Improve backtracking for sbend_face
Sep 6, 2023
b6fee26
Improve backtracking for bend_fringe
Sep 6, 2023
1a53f1f
Improve fringe testing
Sep 8, 2023
25204fa
improve c++ bend fringe
Sep 8, 2023
0e8d838
Improve bend_face map and test
Sep 8, 2023
2fb320a
Simplify bend_fringe
Sep 8, 2023
dd5bdda
Merge branch 'dev' of https://github.com/MethodicalAcceleratorDesign/…
Sep 8, 2023
de639e2
Improve tolerance for straight fringes
Sep 8, 2023
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108 changes: 65 additions & 43 deletions src/madl_dynmap.mad
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Original file line number Diff line number Diff line change
Expand Up @@ -1777,21 +1777,33 @@ function bend_face (elm, m, lw, h) -- [NEWFACE] --
px = px + k0hq*x^2
end

-- This is still not fully revesible in 3rd and 4th order, due to self dependance of px
local dpp = 1 + 2/beta*pt + pt^2
local _pt2 = 1/(dpp - px^2)
local xi = 2*k0hq*sqrt(dpp)*_pt2
local dxi_px = 2*px*xi *_pt2
local dxi_ddel = -2 *xi*(1+pt) *_pt2
local y2 = y^2

x = x / (1-dxi_px*y2) -- this affects reversibility also, for py
px = px - xi*y2
py = py - 2*xi*x*y
t = t + dxi_ddel*x*y2

if sdir == -1 then -- to insure reversal symmetry; horizontal wedge (only sdir) -> PTC uses edir, and if we do this, reversing edir does not give the same result
px = px + k0hq*x^2
-- This is still not fully revesible in 4th order, due to dependancy of x on px and vice versa.
local dpp = 1 + 2/beta*pt + pt^2
local y2 = y^2
local _pt2 = 1/(dpp - px^2)
local xi = 2*k0hq*sqrt(dpp)*_pt2
local dxi_px = 2*px*xi *_pt2

if sdir == -1 then
local npx = px - xi*y2
_pt2 = 1/(dpp - npx^2)
xi = 2*k0hq*sqrt(dpp)*_pt2
dxi_px = 2*npx*xi *_pt2
end

local dxi_ddel = -2*xi*(1+pt)*_pt2

if sdir == 1 then
x = x / (1-dxi_px*y2)
px = px - xi*y2
py = py - 2*xi*x*y
t = t + dxi_ddel*x*y2
else
t = t + dxi_ddel*x*y2
py = py - 2*xi*x*y

x = x / (1-dxi_px*y2)
px = px - xi*y2 + k0hq*x^2
end

m[i].x = x
Expand Down Expand Up @@ -1863,6 +1875,33 @@ function bend_wedge (elm, m, lw_, e) -- [WEDGE] see also [sr]bend_thick --
m.atdebug(elm, m, 'bend_wedge:1')
end

local function bend_fringe_param (dpp, px, py, c2, b0, tfac, only_ky)
local pz = sqrt(dpp - px^2 - py^2)
local _pz = 1/pz
local _pz2 = _pz^2

local xp, yp = px/pz, py/pz
local xyp, yp2 = xp*yp, 1+yp^2
local xp2,_yp2 = xp^2 , 1/yp2

local fi0 = atan((xp*_yp2)) - c2*(1 + xp2*(1+yp2))*pz
local co2 = b0/cos(fi0)^2
local co1 = co2/(1 + (xp*_yp2)^2)*_yp2
local co3 = co2*c2

local fi1 = co1 - co3*2*xp*(1+yp2)*pz
local fi2 = -2*co1*xyp*_yp2 - co3*2*xp*xyp *pz
local fi3 = - co3*(1 + xp2*(1+yp2))

local ky = fi1*xyp*_pz + fi2*yp2*_pz - fi3*yp
if only_ky then return fi0, nil, ky, nil end -- only ky is needed, speed up calculation

local kx = fi1*(1+xp2)*_pz + fi2*xyp*_pz - fi3*xp
local kz = fi1*tfac*xp*_pz2 + fi2*tfac*yp*_pz2 - fi3*tfac*_pz
return fi0, kx, ky, kz
end


function bend_fringe (elm, m, lw) -- [FRINGE_DIPOLE] -- checked
if abs(m.knl[1]) < minang then return end
m.atdebug(elm, m, 'bend_fringe:0')
Expand All @@ -1884,46 +1923,29 @@ function bend_fringe (elm, m, lw) -- [FRINGE_DIPOLE] --
local c2 = b0*fh*2

local dpp = 1 + 2/beta*pt + pt^2
local pz = sqrt(dpp - px^2 - py^2)
local _pz = 1/pz
local _pz2 = _pz^2
local relp = invsqrt(dpp)
local tfac = -(1/beta + pt)
local c3 = b0^2*fsad*relp

local xp, yp = px/pz, py/pz
local xyp, yp2 = xp*yp, 1+yp^2
local xp2,_yp2 = xp^2 , 1/yp2

local fi0 = atan((xp*_yp2)) - c2*(1 + xp2*(1+yp2))*pz
local co2 = b0/cos(fi0)^2
local co1 = co2/(1 + (xp*_yp2)^2)*_yp2
local co3 = co2*c2

local fi1 = co1 - co3*2*xp*(1+yp2)*pz
local fi2 = -2*co1*xyp*_yp2 - co3*2*xp*xyp *pz
local fi3 = - co3*(1 + xp2*(1+yp2))

local kx = fi1*(1+xp2)*_pz + fi2*xyp*_pz - fi3*xp
local ky = fi1*xyp*_pz + fi2*yp2*_pz - fi3*yp
local kz = fi1*tfac*xp*_pz2 + fi2*tfac*yp*_pz2 - fi3*tfac*_pz

local fi0, kx, ky, kz = bend_fringe_param(dpp, px, py, c2, b0, tfac, sdir==-1) -- this method is not perfect.
local ny = 2*y / (1 + sqrt(1-2*ky*y))
if sdir == 1 then
y = 2*y / (1 + sqrt(1-2*ky*y))
local y2 = y^2
local ny2 = ny^2

m[i].x = x + 0.5*kx*y2
m[i].py = py - (4*c3*y2 + b0*tan(fi0))*y
m[i].t = t + (0.5*kz + c3*y2*relp^2*tfac)*y2
m[i].y = y
m[i].x = x + 0.5*kx*ny2
m[i].py = py - (4*c3*ny2 + b0*tan(fi0))*ny
m[i].t = t + (0.5*kz + c3*ny2*relp^2*tfac)*ny2
m[i].y = ny
else -- need to reverse y-dependence
-- This is still not fully revesible in 3rd and 4th order, due to self dependance of y
-- This is still not fully revesible in 5thand 6th order, due to self dependance of py -> results in max error of 1e-11 and 2e-9 for 5th and 6th order respectively
local new_py = py + (4*c3*ny^2 + b0*tan(fi0))*ny
fi0, kx, ky, kz = bend_fringe_param(dpp, px, new_py, c2, b0, tfac) -- this method is not perfect.
local y2 = y^2

m[i].x = x - 0.5*kx*y2
m[i].py = py + (4*c3*y2 + b0*tan(fi0))*y
m[i].t = t - (0.5*kz + c3*y2*relp^2*tfac)*y2
m[i].y = 0.5*y * (1 + sqrt(1-2*ky*y))
m[i].y = y - y2*ky/2
end
end

Expand Down