OPTICIAN

          A COMPUTER PROGRAM FOR BEAM OPTICAL PROBLEMS

            Nicholas R. White, after T.J.L. Greenway.

               (C) Nicholas R. White, 1983,1986.





1. Introduction

        "Optician" is an interactive program which allows the user to
trace the trajectories of single rays or of beam  envelopes through
any series of beam optical elements, with output to the display or
plotter or both. Various adjustments or optimising routines are
available which enable the desired trace to be obtained on the display
and a hard copy then to be produced on the plotter. The program is
developed from the Oxford beam optics program Optryk by Tom Greenway 1
which used routines based on "Rayplot" by K.H. Purser2.
..page
2. Operating the program.

        The program OPTICIAN is on a diskette containing DOS 2.0 and a
startup file. Place it in drive A and switch on or reboot the system.
Press the (Caps Lock) key, since the program only recognises upper case
letters as valid commands.  Place a diskette for data files in drive B if
required. After exiting, the program may be restarted by typing

  OPTICIAN(CR)

In this document (CR) is used to represent the carriage return key.

        The program starts by going through an input sequence once to
specify all necessary parameters, after which various options become
available. On entry to the program, when the element sequence is being
specified or when the option switches are available (indicated by *)
entering H(CR) (help) will type a summary of the options.

        On entry the program types

Input from:

to request the form of data entry; the response should be 
              T(CR)
                      for input from the terminal keyboard, or
              D(CR)
                      for input from a disk file (which must have been
created during a previous run). Any other input will cause a Help
message to be typed to the screen.

        For terminal input a Filename, (the default diskette drive is B)
and extension (e.g. TESTFILE.MK3) and a Title (up to 60 characters) must
be given; these appear on subsequent listings or plots, and the filename
is the name of the file on which data may later be stored by the O
(Output) command, unless it is later changed by the N (new Name)
command.

        For disk file input Filename is the name of the file read.
WARNING: an error in the typing of the filename causes exit from the
program, which is inconvenient.
..page
         When entering data from the terminal, an element sequence is
first specified, consisting of a list of allowed beam optical elements
in the order in which they are encountered by the beam. The element
types at present available are:

       Full title:                                Abbreviation:
        Ion source................................ I
        Drift length.............................. D
        Quadrupole singlet lens................... Q
        Solenoid lens............................. S
        Focal Length (thin Lens).................. F or L
        Bending magnet (median plane horizontal).. M
        Axial rotation (about z axis)............. R
        Accelerator Tube.......................... A or T
        Gas or foil stripper (Scattering effect).. G
        Electrostatic bend (Cylindrical).......... B
        End of sequence........................... E

One element is specified per line. Only the initial letter is needed. If
an illegal character is typed in the element sequence this sequence is
aborted and a reminder of the allowed elements is typed; if H is typed
in the sequence this reminder is immediately typed, but the sequence
must be restarted. The maximum number of elements that can be stored is
50.

        The program then asks for the parameters of the various elements
specified.

3. Data entry

        When the program requests data to be entered it will be accepted
in free format. The values may be entered on one line, each
value being terminated by comma, or on successive lines.  A value must be
given for every parameter, even if it is zero.

        Those parameters which are altered by the optical elements
(charge, energy, momentum, etc.) are updated automatically.

4. Ion source.

        This should be the first element in the sequence. Subsequent
ion sources are allowed (up to a maximum of six); after each source a
new set of beam coordinates is started (either beam envelope or single
ray).

        Injection energy (MeV); specify the beam energy at the source
and let the program look after it thereafter.

        Charge state (in units of e); usually 1 at the beginning,
or the current value at any later source in the sequence. It may be
changed in subsequent accelerator tubes.

        Mass (AMU); can only be changed by another ion source.

        Current (mA); This is important in the optics of accelerator
tubes; it is assumed that the beam is 95% space-charge neutralized
elsewhere. NOTE: For beams typically encountered in tandem
accelerators space charge is insignificant. In systems where the
optics is sensitive to the current, care must be taken to provide
reliable traps for neutralizing particles, and design the optics to
tolerate fluctuations in current.

        Momentum (MeV/c) is calculated by the program from the input
data.

        The program then asks whether a single ray or a beam envelope is
required. The six starting coordinates (x,x',y,y',DelptaP,DeltaL) are
then requested. For a beam envelope these are the projctions of a six
dimensional upright ellipsoid on these axes. A beam is therefore assumed
to start at a waist. For many beams the last two coordinates are not
relevant, and only the values for (x,x',y,y') need be entered, followed
by two zeros.

       The user is expected to have a working familiarity with this
conventional beam optical notation. The beam central ray is the z-axis,
which may be curvilinear, and the x- and y- coordinates are measured
from it; x' and y' are the angular divergences from the z-axis. The
program makes the assumption that divergences are sufficiently small
that an angle is equal to its tangent. This assumption is usually an
excellent approximation; the error at 200mrad is 10%. For more details,
see reference 3.

5. Drift length.

        Enter the length in meters. The program can handle negative
lengths (treated as a single step in plotting, i.e. a straight line in
the negative direction). Zero lengths may be entered as dummies for
later insertion of different elements by the R (rearrangement) command.
It is often convenient to divide long drift lengths into two or three
shorter lengths, so as to place a marker on the plots.

6. Quadrupole singlet.

        Enter length in meters, and dimensionless strength parameter K =
kl where k2= g/BR (g = magnetic field gradient, BR = beam rigidity).
Electric field gradient = g*v (velocity in m./sec.). The trajectory in a
converging quadrupole is a sinusoid; K is the number of radians of this
sinusoid to occur within the quadrupole.

        Since the quadrupole strength contains a beam rigidity factor
focusing occurs independent of momentum or charge state. To investigate
the effect of defocusing for different beams with the same quadrupole
current (constant g) the strength should be adjusted in inverse
proportion to the square root of the beam rigidity (BR).

        Initial strength parameters are rather a matter of trial and
error; for a doublet it usually turns out to be around 0.6. Enter a
positive strength for a singlet converging in the horizontal plane,
negative for diverging.

        It is possible to enter coupled quadrupoles into the sequence.
A doublet is normally constructed by specifying two free singlets; the
strength of these singlets may later be optimised to find beam waists.
For a triplet the normal arrangement is for the first and third
singlets to have the same excitation, therefore to construct a triplet
in the program specify two free singlets and a third singlet coupled to
the first. Thus the length and strength of two singlets are given (the
first usually being shorter than the second) and for the third singlet
a coupling coefficient is entered in place of the strength; this is
usually +1.0 for a horizontally converging third singlet, and -1.0 for
one diverging. Then in response to the question

Is this quad coupled to a previous one?

enter Y(es) for the third singlet, and give the sequence number of the
first singlet. Later when using the quadrupole optimising routine the
sequence numbers of the first and second elements are given as variable
elements,and the third element remains automatically coupled to the
first. Similarly quadrupole quartets or other multiplets may be
constructed, keeping two free singlets for the optimising routine. Note
that coupling can only be specified to a quadrupole earlier in the
sequence. Coupled singlets may later be respecified as free using the R
(rearrangement) command.

7. Solenoid lens.

       A solenoid lens focuses a beam but also rotates it; this is
fully taken into account. The length and strength must be specified in
a similar way to that for quadrupoles. The program will calculate the
required magnetic field strength if the data are printed out on the
printer.

8. Magnet.

        Uniform field (index N = 0) and non-uniform field magnets are
treated, the bending plane being horizontal (x plane). Where magnets
occur with different bending planes an axial rotation may be placed
between them.

        The effect of finite fringing fields is to reduce y-focussing.
To allow for this effect, an algorithm of Enge3 is included. The
program will ask for the pole gap in mm, and a field integral I2. This
integral is typically 0.45 for a sharp edged pole, but may be as large
as 0.75 for a Rogowski profile or in a magnet which saturates. Do not
place undue faith in the predictions for magnets whose field integrals
are as yet unknown. Do not use pole gaps greater than one fifth of the
bending radius, as further corrections may then be needed. Within
these limitations, results have been excellent.

9. Axial rotation.

        Rotates the beam around the z axis. Angle in degrees. This is
very useful in the following situations:
-      if two bending magnets bend in different planes,
-      if an acceleration tube has an entrance slit which is not
       horizontal (as the program assumes),
-      to investigate the effect of quadrupole misalignment.


10. Accelerator tube.

        Accelerator tubes can be entered with various options for the
focusing effect at the tube entrance and exit. If the entrance or exit
is gridded there is no focusing effect; enter 0 for entrance or exit
lens. If the entrance or exit is the normal circular aperture, enter 1.
A correction factor, determined from ray plotting through a potential
field determined by a relaxation calculation, can be applied to the
aperture lenses,6,7; for small or zero diameters this factor
approaches 1, when the same focusing as given by Larson's program
OPTIC should be obtained. The correction factor also approaches 1 when
the aperture lens effect is weak. HVEC used tubes with horizontal slot
electrodes, except at the low energy entrance; this effect can be
obtained by entering 2 for the entrance and exit lenses. A horizontal
slot has no focusing effect in the horizontal plane, and twice the
focussing effect of a circular aperture in the vertical plane.
       Each change of field gradient should be represented by a section
of accelerator tube, with the appropriate apertures at entrance and exit
(circular or slot). At the junction of the tube sections the diverging
exit lens and the converging entrance lens will combine to form the
correct focusing effect for the change in field gradient (to a good
approximation). Entering other than 0, 1 or 2 for the lens effect gives
a typed reminder, and the correct code may be retyped.

       Within an accelerator tube, the beam is assumed to be
unneutralized, and space charge is taken into account, assuming a
uniform current distribution. It may be necessary to allow extra short
accelerator tube lengths to simulate an electron trap at the negative
end of accelerator tubes used for positive ions.

11. Focal length (thin lens).

        Enter the focal lengths in the horizontal and vertical planes,
FX and FY. These will usually be equal, representing a cylindrical
electrostatic lens. Zero focal lengths are interpreted subsequently as
meaning zero strength, i.e infinite focal length.

       While this device is idealized, and only approximately valid as a
representation for Einzel lenses, it has other important uses. For
example, if the required starting coordinates are NOT an upright beam
ellipse (i.e. a waist), the procedure is to specify an ion source of the
correct size, to enter a divergence which gives the correct emittance,
and then to alter the divergence by means of a thin lens as element 2.
This procedure also allows slit geometry sources to be well represented.

12. Gas or foil stripper (scattering).

        Either foil or gas stripper may be specified; since lateral
displacement of the beam in a long gas stripper turns out to be
negligible in the case of tandem strippers only angular scattering at a
plane normal to the z axis is considered. Zero thickness may be
specified, to give no scattering.

        The scattering is calculated according to a Thomas - Fermi
potential9 and incorporated as a RMS width assuming a gaussian
distribution. Thus if the initial beam envelope corresponds to a RMS
width the scattered beam envelope will still correspond to the RMS
width. However for very thin scatterers a Gaussian distribution
underestimates the width, there being a large proportion of the beam in
the tail scattered at large angles. Even for fairly thick scatterers
the RMS width contains only about 20% of the beam, if one considers an
integration of the density function over x, x', y, and y' to the RMS
width. Since the effect of a stripper is to increase the emittance of a
beam, the stripper is ignored when a single ray is being transmitted.
..page
13. Options.

        At the end of the data entry for the element sequence the
option become available, indicated by:

*

The replies to this prompt are listed below; some can include element
sequence numbers as numeric arguments.

(blank)(CR) is no-op.

A(CR)    New axes

         Clears the plot. Next time D is typed the screen is cleared
         and new axes are plotted.

C(CR)    Coordinates

         Enter a new set of ion source coordinates: Mass, charge,
         initial energy, current, ray or envelope, and (x,x',y,y',
         DeltaP,DeltaL).  The screen is not cleared at the next D, thus
         successive traces may be overlaid on the same plot. Cn(CR) to
         change coordinates for ion source no. n.

D(CR)    Display

         the current plot on the screen. The top half of the screen
         shows the trajectory or beam envelope in the horizontal plane,
         and the lower half the vertical plane, with the particles
         travelling from left to right. In the case of single rays it
         is possible to cross the axis, so horizontal and vertical
         should be determined from the starting position. The positions
         of the element boundaries are shown with a label indicating
         which element it is. The switches C, F, M, Q, S and T can be
         called to change rays or certain element parameters which
         affect focusing, after which a D will cause the new ray to be
         overlaid on the screen or plot. This can be repeated several
         times; the A command should be used to clear the screen
         regularly.

E(CR)    Exit

         from the program. Clears the screen.

F(CR)    Focus

         Change the focal length of a thin lens. F5(CR) allows lens
         sequence no. 5 only to be given a new focal length. The screen
         is not cleared at the next D, thus successive traces may be
         overlaid on the same plot.

G(CR)    Gas (or foil) stripper

         Allows the stripper thickness to be varied. The screen is not
         cleared at the next D, thus successive traces may be overlaid
         on the same plot. G4(CR) allows stripper sequence no. 4 only
         to be given a new thickness.


H(CR)    Help

         types a brief summary of the options.

I(CR)    New Input

         Goes to the beginning of the program to input a new element
         sequence. Automatic A is given.

L(CR)    List

         A detailed listing of the current element sequence and element
         parameters is sent to the line printer, together with a list
         of the particle or beam coordinates at the end of each element
         and the distance and size of the nearest beam waist.

M(CR)    Magnet

         Change magnet pole tip angles and index to specified new
         values. Typing M6(CR) allows magnet sequence no. 6 only to have
         its pole angles changed. The screen is not cleared at the next
         D, thus successive traces may be overlaid on the same plot.

N(CR)    New Name

         A new filename and title may be given for the current data.
         The creation date is updated. These items appear as headings
         on plots and listings, and Filename is used for input and
         output of data to the disk. NOTE: this command in itself does
         not save the data. Remember to type O.

O(CR)    Output

         Sends the current data (element sequence and parameters) to
         the diskette where it is stored on a file with the current
         Filename.

P(CR)    Plot

         the current plot on the Epson dot matrix printer.  If there
         has been no previous plot or if a new frame has been started,
         plots new axes followed by the trajectories. Further rays may
         be overlaid without replotting axes. This command is
         otherwise the same as D. In subsequent use of D  the first
         trajectory displayed will be the last one plotted.
         NOTE: this produces high resolution labeled plots. Low
         resolution plots can of course be obtained with the IBM PC
         PrtSc key at any time. The P command will print a list of
         plotting captions on the plinter, but writes the plot to a
         disk file. After exiting the program, a utility called PLOT
         is invoked automatically, and this completes the plotting
         process. High resolution plots take several minutes to
         complete, and cannot be interrupted.
..page
Q(CR)    Quadrupole strength

         Option for changing any quadrupole to a specified new
         strength, or to optimise a pair of singlets (to which any
         number of other quads may be coupled) to form a waist at a
         specified position after the end of a given element - the
         reference plane.The computer asks which option is required: for
         the first option it asks for a new strength for each singlet in
         turn, or a new coupling coefficient if it is coupled. For the
         second option the two singlets to be optimised are chosen and
         the distances from the reference plane to the required waist
         positions (x and y) are specified (left negative, right
         positive). An iteration process then optimises the two singlet
         strengths, and the final strengths are typed out. By changing
         the starting strengths followed by a second Q to optimise again
         other waist conditions may be found, as it is possible to
         obtain either a broad waist with low divergence or a narrower
         waist with correspondingly higher divergence. Typing Qn(CR)
         allows a new strength to be specified for quadrupole sequence
         no. n only. The screen is not cleared at the next D, thus
         successive traces may be overlaid on the same plot.

R(CR)    Rearrangement

         of element sequence. Enables corrections to be made for typing
         errors at input, elements to be changed from one type to
         another or element parameters to be changed. The computer asks
         which option is required: typing -1 allows addition of a
         further sequence of elements to continue after the present
         sequence; this allows long sequences to be built up step by
         step, getting the required result for a simple case before
         making it more complex. Typing an element sequence number
         allows that element to be changed to a different type, or the
         parameters of that element to be changed. (CR) returns to the
         option switches (*). An automatic A is performed. Typing
         Rn(CR) allows element sequence no. n only to be changed.

S(CR)    Solenoid

         Change the strength of solenoid lenses. The screen is not
         cleared, and successive plots may be overlaid on the same
         plot. S7(CR) changes the strength of only solenoid sequence
         number 7.

T(CR)    Tube

         Change potential across accelerator tube or charge state of
         particles. The screen is not cleared at the next D, thus
         successive traces may be overlaid on the same plot. Tn(CR)
         allows tube sequence no. n onlyto be changed.
..page
W(CR)    Waist

         For a single ray types out the particle coordinates at the end
         of the specified element, or for a beam envelope types out the
         distance from the spcified element to the nearest beam waist,
         together with waist radii and divergences. Type Wn(CR) for the
         sizes at the end of element no. n.

         The overall transfer matrix from the source to the end of a
         given element n can be viewed by typing W-n(CR).

Y(CR)    Yanks the current sequence of element parameters onto the
         screen. The display will be lost. Yn(CR) displays data for
         element n only, and preserves the display.
..page
References

1)    T.J.L. Greenway, OPTICS program, Oxford Nuclear Physics internal
      report.
2)    K.H. Purser, RAYPLT program - private communication.
3)    A Septier, ed. Focusing of Charged Particles, Academic Press
      (1967)
      A.P. Banford, Transport of Charged Particle Beams, Spon (1966)
4)    K.L. Brown, SLAC report no. 75 (1971)
5)    J.D. Larson, I.E.E.E. Trans. NS-18 No.3, 1088 (1971)
6)    M.M. Elkind, R.S.I. 24, 129 (1953)
7)    P.J. Stenning & C.W. Trowbridge, Reading University / Rutherford
      Laboratory Report RU/RL 1 (1968)
8)    T. Joy, N.I.M. 106, 237, (1973)
9)    P. Sigmund & K.B. Winterbon, N.I.M. 119, 541 (1974) and 125, 491
      (1975)