**4.2.2 Target Hall Baffle**

**4.2.2.1 Baffle Functions and Requirements**

The baffle must:

-   Prevent mis-steered primary proton beam from causing damage to the
    horn neck and target cooling/support components.

-   Be capable of operating continuously with 3% beam scraping at design
    luminosity.

-   Withstand full intensity of beam for a number of pulses it will take
    to detect mis-steering of beam and shut beam off.

-   Incorporate monitoring that will shut beam off in case of continued
    large loss of beam on baffle. It may be useful for efficient running
    that loss of one pulse on baffle not turn off the beam.

-   Construction and alignment tolerance of hole through baffle must be
    0.5 mm or better.

In addition:

-   Incorporate monitoring that allows detection and monitoring of
    beam-baffle scraping at order of 1% accuracy. (E.g. if 2% of the
    beam is being scraped, measure (2+/-1)%). Since actual full power
    beam running is expected be around 2x10^13^ during the first couple
    years running, this means an accuracy of +/-2x10^11^ or better.

-   Incorporate monitoring that allows a crosscheck of alignment via
    e.g. low intensity beam-scan to 0.5 mm.

-   Have the baffle move along the beamline with the target, as this
    increases the available target travel (the overall length for
    extraction of a broken target/baffle module is limited, and by
    having the target stick out one end of the carrier at one extreme of
    motion and the baffle stick out of the carrier at the other extreme
    one makes maximum usage of this length).

**4.2.2.2 Baffle hardware design**

The baffle, **Figure 4.2-4**, is mounted with the target to eliminate
the expense of another module to support and align it. The baffle and
target can be pre-aligned to each other before attachment to the module,
and move as a unit. The baffle construction tolerance is 0.2 mm RMS; the
goal for overall baffle position accuracy is 0.5 mm, including thermal
effects, survey tolerance, and carrier wobble.

.

**Figure 4.2-4** ![](media/image1.wmf){width="6.0in"
height="4.458333333333333in"}Baffle. 150 cm long, 11 mm diameter hole,
57 mm diameter graphite core, 61 mm diameter aluminum casing. Cooling
fins not shown. Thermocouples will be located near the downstream end of
the baffle

###### Baffle hole size, baffle location -- beam accident geometry

The baffle hole is made as large as possible, while still providing
protection to the horn and target. **Figure 4.2-5** and **Figure 4.2-6**
show the layout of the baffle relative to the target and horn.

**Figure 4.2-5**![](media/image2.wmf){width="4.198611111111111in"
height="6.0in"} Plan view of baffle, target, and horn geometry. Since
target is rectangular rather than cylindrical, limits of its horizontal
and vertical extent are shown. Note large factor between horizontal and
vertical scales

![](media/image3.wmf){width="5.986111111111111in" height="7.75in"}

Figure 4.2-6 Beam-eye view of baffle inner radius and comparison to beam
spot, target fin, horn neck, and target cooling and support structure.

The horn protection system actually consists of two baffle locations, a
relatively large opening after the last bend string (but unfortunately
before the last quad), and a second baffle in the target hall. Peter
Lucas produced a spreadsheet that takes into account the magnetic field,
and gives the maximum radius that the beam could reach while still
passing through the two baffles. These limits are set entirely by the
two baffles and the intervening magnet, and do not try to identify
magnet failures that could actually produce these deviations. Examining
some variations run by Adam Para, the pattern is roughly that the fully
protected region is the baffle radius plus (0.5 mr horizontal, 0.7 mr
vertical) times the distance downstream of the baffle.

**Table 4.2-2** lists three items to be protected by the baffle. In it,
are derived maximum baffle radii using the above rule of thumb for two
cases: (1) having the baffle close to the target, and moving with the
target, or (2) at a fixed upstream location which would still allow
target movement to the HE location without moving the baffle. Baffle
radius is reduced by 0.5 mm to allow for alignment tolerance. Numbers
are in coordinate system where horn 1 starts at Z=0cm (i.e. the GNUMI
Monte Carlo coordinate system). The horn neck is at (Z,R) = (0.8m,9mm);
the top edge is shadowed by the target, so only the horizontal edge is
included in the calculation. The target cooling line solder starts at
(Z,R) = (-0.35m,7.5mm) at top and bottom of graphite fin; after some
distance down target, the graphite contributes to shielding the tube.
The cooling loop tube between supply and return is at the end of the
target (Z,R) = (0.6m,7.7mm), and is exposed in the horizontal direction.

  ---------------------------------------- -------------- ---------------
  ***Baffle hole R(max)***                 Baffle Z=-2m   Baffle Z=-5m

  Horn 1 neck, X direction                 7.1 mm         5.6 mm

  Target cooling tube, Y direction, LE     5.8 mm         3.7 mm
  position                                                

  Target cooling loop, X direction, LE     5.9 mm         4.4 mm
  position                                                
  ---------------------------------------- -------------- ---------------

Table 4.2-2 Maximum baffle hole radius allowed for different layouts of
baffle, horn and target.

From the above table, it is seen that a 5.5 mm radius baffle hole
protects the horn for all baffle locations, for all different energy
beams. If the target and baffle move together, then a 5.5 mm radius
baffle will also protect the target for all beam configurations; however
a fixed location baffle would require a smaller hole to protect the
target. It is also seen that the X and Y requirements are very similar,
and a circular hole thus makes sense. From the above arguments, the
baffle is mounted near the target, moves with the target, and the radius
of the hole is selected to be 5.5 mm.

In the current layout, the baffle ends at -103 cm in the Monte Carlo
coordinate system, or 68 cm before the leading edge of the target
vertical fin.

###### Baffle material

Calculations have been done of energy deposition, heat rise, and stress
for the standard NuMI beam (4e13 protons in a 0.7 mm sigma-x 1.4 mm
sigma-y beam spot) hitting Nickel, Copper, Aluminum, and Graphite.
Nickel and Copper are clearly unsuitable. Aluminum is marginal; it would
exceed its yield point and creep modestly with accident pulses \[ref.
[^1]\]. Graphite is satisfactory \[ref. [^2]\]. Beryllium would also
work, but is rejected because it would generate mixed waste
unnecessarily. We have selected Graphite; it is reasonable to use the
same grade selected for the target, ZXF-5Q, since we already have
experience with it in the target beam test.

###### Baffle outer radius

IHEP has proposed shrink-wrapping the graphite in a long aluminum tube
\[ref. Error: Reference source not found\]. This provides good thermal
contact with the graphite that will be maintained under beam heating in
spite of the larger thermal expansion coefficient of aluminum. Also it
can be done with high accuracy. The technology they describe would limit
baffle diameter to 60 mm; 60 mm would appear to be a reasonable match to
NuMI requirements. The graphite diameter is 57.1 mm, which is a standard
stock graphite rod size.

###### Baffle length

Calculations have been done to find out how long the graphite baffle
must be to protect the horn inner conductor, the target cooling tube and
solder joint to the graphite, and the target ceramic. The position of
the baffle was also varied. The position/length selected is that which
has the upstream end of the baffle as close to the target as will still
provide a good safety margin. This allows the greatest possible target
motion. The result chosen is150 cm long baffle with 68 cm spacing
between baffle and target fin. Curiously, extending the baffle length in
the space between target and baffle further actually makes the energy
deposition in the target fixturing worse, although it reduces the energy
deposition in the horn neck. Please see \[ref. Error: Reference source
not found\] for derivations of acceptable temperature rises. **Figure
4.2-7** and **Figure 4.2-8** include temperature rises for baffle
lengths and positions calculated after \[ref. Error: Reference source
not found\] was written. The chosen operating point as shown in **Figure
4.2-8** corresponds to (a) cooling pipe steel stress of 50 MPa compared
to 340 MPa yield, (b) Aluminum horn neck stress of 70 MPa compared to
210 MPa yield, (c) ceramic insulator stress of 30 MPa compared to 170
MPa yield, and (d) target solder joint temperature rise of 70 K over
approximately 30 deg C operating temperature compared to 340 deg C
melting point.

**Figure 4.2-7**![](media/image4.wmf){width="5.952083333333333in"
height="5.3694444444444445in"} Temperature rise of protected components
for an accident spill as a function of the length of the baffle. The
distance Lbt between the downstream end of the baffle and the target
vertical fin is 176 cm (circles), 86 cm (boxes), and 41 cm (triangles).

![](media/image5.wmf){width="6.0in"
height="5.486111111111111in"}**Figure 4.2-8** Temperature rise of
protected components for an accident spill as a function of the position
of a 1.5 m long baffle. Lbt is the distance from the end of the baffle
to the start of the target vertical fin. The chosen design value of 68
cm is marked.

###### 

###### Baffle atmosphere and windows

\[ref. Error: Reference source not found\] documents that the maximum
temperature in the core of an accident shower along the inner edge of
the baffle is 344 deg C, at which temperature no detectable oxidation is
expected. The oxidation threshold (temperature resulting in 1% weight
loss in 24 hours) for ZXF-5Q is 450 deg C. Hence an inert atmosphere in
the baffle is not required.

Beryllium windows are provided to prevent erosion of the graphite by the
strong wind in the target pile. A ventilation hole is provided to
prevent air pressure buildup. To help keep ventilation hole clear of
debris, the hole should not be oriented upward; to help prevent
contamination falling out of the hole, it should not be oriented down;
hence we plan to orient the hole horizontally.

###### Baffle thermal warp

A thermal gradient laterally across the baffle can be caused by
azimuthally asymmetric beam loss, air flow, or cooling fin contact. This
would cause the baffle to warp. The following arguments indicate such
effects are not a problem for us.

A zeroth order model with a linear temperature gradient across the
cylinder gives a warp of the center relative to the ends of (αTL^2^/8w)
where α is the coefficient of thermal expansion, T is the maximum
temperature difference, L is the length of the baffle, and w is the
width of the baffle. For a warp of 0.5 mm, this implies a temperature
difference of 13.3 K for graphite across the baffle. Numerically
modeling non-realistic extreme cases where the entire fin cooling was on
one half of the baffle or the entire heat deposition was on one half of
the baffle for 3% continuous scraping gave only a few degree temperature
differences even at the higher temperature downstream end of the baffle.
Hence this effect can be safely ignored.

# 4.2.2.3 Baffle cooling and monitoring

Calorimetric methods are a simple and direct way of monitoring the beam
loss on the baffle. For this to work, the cooling of the baffle should
be adjusted so that temperature rises are easily measured with standard
thermocouples but the baffle will not overheat. The simplest is to rely
on heat transfer to the existing air flow, with the addition of fins to
increase the heat transfer. However, heat transfer efficiency is hard to
precisely calculate a priori, so a large safety factor should be built
in for the operating parameters.

Figure 4.2-9 shows the energy distribution when beam hits the front of
the baffle \[ref. [^3]\]. This corresponds to an average temperature
rise of 11 K per pulse at the downstream end of the baffle for full
power beam. Since the largest temperature rise is downstream, the
monitoring thermocouples should be mounted near the downstream end.

![](media/image6.wmf){width="6.0in"
height="5.402777777777778in"}**Figure 4.2-9** Energy deposited in baffle
(J/cm3/pulse) as a function of position along baffle for 4e13 protons
hitting baffle, averaged over 3 cm baffle radius and 30 cm long baffle
segments. Integral is 42 kJ/pulse, corresponding to 22 kW at 1.87 second
repetition rate, or 5.5% of the 400 kW total beam power.

To first order, the time constant for heat transfer to the cooling air
is (Vdc/Ah), and the asymptotic temperature rise is (PV/Ah), where V is
the volume of graphite, d is the density of graphite 1.8 g/cm3, c is the
specific heat capacity of graphite 0.7 J/gK, A is the surface area of
the graphite segment, h is the heat transfer coefficient from baffle to
air, and P is the power deposited per unit volume. For a 3 cm radius
cylinder, V/A = 1.5 cm. The cooling air flow along the surface of the
baffle is about 4 m/s, which would give h\~12W/m2K for flow parallel to
a fin-less cylindrical baffle \[ref. Error: Reference source not
found\]. The actual flow pattern is hard to predict, and with transverse
flow the heat transfer coefficient could be double this. For use in
selecting a strategy, a hypothetical fin with five times the heat
transfer of the cylinder is chosen as a reasonable operating point, and
shown in comparison in the table. The cooling air temperature will be
about 16 deg C. Note that \[ref. Error: Reference source not found\]
includes full three-dimensional modeling of the heat transfers, with
results that agree well at the downstream end of the baffle with the
simple approximation given here.

The baffle fin design has not been finalized, but Figure 4.2-10 shows a
concept. It consists of two half rings 1.5 mm thick with pins 2 mm in
diameter. Pins of 15 mm height are located with period 7 mm along the
circumference and 9 mm along the baffle. The internal radius of a half
ring is the same as the external radius of the baffle casing. These half
rings are pressed to the baffle casing via a stainless steel clamp,
providing pressure about 10-20 MPa. Such a pressure should provide a
good thermal contact between radiator and casing. Another method of
providing a good thermal contact is use of a 50 micron thick Indium
film. The estimate of effective heat transfer coefficient of the pin
radiator is 300 W/m^2^K at 4 m/s air velocity, which implies that only
about 20% of the surface area of the baffle would have to be covered
with the fins to achieve the desired heat transfer shown in Table 4.2-3.

  ---------------------------------- -------------------- ----------------
                                     No fin, air flow     Fin on baffle
                                     parallel             

  Heat transfer coeff. (h)           12 W/m^2^K           60 W/m^2^K

  Time constant toward asymptotic    1575 sec             315 sec
  temperature rise                                        

  Asymptotic temperature rise,                            
  downstream end                                          

  Full power accident                (9291 K)             (1858 K)

  3% continuous scraping             (278 K)              56 K

  1% desired monitoring accuracy     93 K                 19 K

  Temperature rise per pulse,        11 K                 
  downstream end, full beam power                         
  ---------------------------------- -------------------- ----------------

**Table 4.2-3** Thermal parameters for two different air heat transfer
coefficients. Temperatures in parenthesis ignore radiative cooling, are
prevented from occurring by a 120 deg C thermocouple limit input to beam
interlock, but are included for illustration.

**Figure 4.2-10**![](media/image7.wmf){width="5.986111111111111in"
height="7.541666666666667in"} Section of pin radiator. 20% to 30% of the
baffle surface will be covered with such radiators.

###### 

###### 

###### Accident scenario

To prevent damage to the aluminum baffle tube, an interlock will be set
to prevent further beam pulses at a thermocouple readback of about 120
deg C. The interlock could be set lower if found to be operationally
desirable. This would prevent more than at most a dozen continuous
accident pulses; however the interlock will probably not be set tight
enough to trip the beam from a single accident pulse. With the fin, the
baffle will cool off in a few minutes, allowing one to turn the beam
back on quickly.

###### Continuous scraping

We are optimistic that beam scraping will be low. The fin design
nevertheless would allow 3% continuous beam scraping with a safety
factor of 2 in the heat transfer coefficient h before reaching the 120
deg C trip point.

The 19 K temperature rise per 1% beam loss is an order of magnitude
larger than needed for monitoring the beam loss at the required level,
providing a large safety factor on the value of h being larger than the
design specification.

Backgrounds to the calorimetric monitoring of the baffle scraping have
also been calculated. The energy deposit in the baffle is 0.10
J/cm3/pulse for 1% scraping, compared to 0.04 J/cm3/pulse from
interactions in the target pile air and 0.0002 J/cm3/pulse backscatter
from the target \[ref. Error: Reference source not found\].

Note that the thermal monitoring does not give pulse-by-pulse monitoring
of the scraping, but an average with a few minute time constant. We have
not yet found an argument showing a necessity for pulse-by-pulse
monitoring of scraping.

###### Calibration

The actual temperature response of the baffle will be calibrated during
commissioning by steering 100% of the beam at low intensity on to the
baffle. Note that a constant beam intensity should be maintained for a
period of several time constants for this measurement.

###### Commissioning alignment scan

The fin parameter set also allows an alignment check of the baffle via
beam scan during commissioning, or whenever one wants to recheck
alignment. It is conservative to turn down beam power during scans; beam
intensity as low as 8x10^11^ protons per pulse is easy to achieve. Such
a single pulse (2% of maximum beam) into the baffle would produce only a
0.2 K temperature rise in the baffle, so one would need to use a large
number of pulses per point (say 30 over a one minute period), or else a
higher intensity beam (in which case one could limit the repetition
rate) to produce a robust thermocouple response. With the standard 1 mm
RMS beam spot, an alignment check accuracy of a fraction of 1 mm would
be expected, based on experience with similar temperature scans done
during the NuMI target test.

Usable signals from the alignment check baffle scan will most likely
also be detected in the horn 1 alignment ionization chamber and the
hadron monitor in front of the absorber, providing redundancy.

Since the baffle and target are pre-aligned on a common carrier, the
combination of baffle scan and Budal-monitor target scan can demonstrate
that the combined baffle/target system is at the correct angle as well
as in the correct position.

# 4.2.2.4 Effect of scraping on the neutrino spectrum

The effect on the neutrino spectrum of beam tails hitting the baffle has
been modeled in GNUMI, and is illustrated in **Figure 4.2-11**. The
effect of scraping is mostly significant between 5 GeV and 8 GeV. In a
10-ktyear exposure, there will be of order 500 events in this range
collected in the MINOS far detector, giving a statistical error of 4%.
Thus knowing a scraping correction to 1% accuracy would keep the
systematic error negligible compared to the statistical error. As shown
in the figure, 1% beam scraping produces about a 1% change in the double
ratio (beam scraping correction), hence measuring the scraping to +/- 1%
of the total beam power is a reasonable specification.

![](media/image8.wmf){width="2.8194444444444446in"
height="2.9305555555555554in"}**Figure 4.2-11** Effect of various
amounts of beam-baffle scraping on neutrino spectrum. Top plots show
spectra separately for 100% of beam on target or baffle. (Mark Messier,
6/12/02)

It would be nice to keep the scraping to less than 1%, so that no
correction at all would need to be applied. For a gaussian beam with 1
mm RMS, 99% of the beam is within 3 mm radius. In our case, the baffle
hole is 5.5 mm radius, and even after allowing for 0.5 mm alignment
tolerances the loss from a gaussian beam would be negligible. However,
only experience with the real beam will tell us if there are significant
non-gaussian tails, or jitter in the beam position that cause losses on
the baffle.

Note this simulation had baffle to target distance of 37 cm instead of
our current choice of 68 cm, but that should have only a minor effect.
In a similar study with the baffle a couple meters further back, Brajesh
Choudhary found the scraping sensitivity to be twice as large, which may
be another motivation for keeping the baffle close to the target.

References

[^1]: Thermal Stress Analysis of Numi Baffle -- II, MSG-EAR-0282, Bob
    Wands, 4/2/01 and Thermal Stress Analysis of NuMI Baffle,
    MSG-EAR-00279, Bob Wands, 11/8/00.

[^2]: [Technical Design of the Target Pile Protection
    Baffle-draft](http://beamdocs.fnal.gov/cgi-bin/public/DocDB/RetrieveFile?docid=729),
    S.Filippov, V. Garkusha, R. Gibadullin, F. Novoskoltsev, I.
    Ponimash, T. Ryabova, V. Zarucheisky, (IHEP) 4/30/02.

[^3]: MARS Simulation: Baffle Heating, B. Lundberg, 6/9/02.