**HELIUM BACKGROUND IN THE D-ZERO DETECTOR**

**RELATED TO THE**

**PHOTOMULTIPLIER TUBES**

D-ZERO ENGINEERING NOTE \# 3823.130-EN-490

> Approved :

Kurt Krempetz, PPD/ETT/D0 Upgrade/Mechanical group leader

> April 9, 1998
>
> Author: Russ Rucinski
>
> PPD/ETT/D-Zero Upgrade project
>
> APPENDIX
>
> April 8, 1999
>
> Author: Jason Lambin
>
> PPD/ETT/D-Zero Upgrade project
>
> **[Summary]{.underline}**

+-------------+----------------+------------------+-------------------+
| **Source**  | #### M         | **Max.           | **Effect on       |
|             | ax. Continuous | Discrete**       | Tubes**           |
|             |                |                  |                   |
|             |                |                  | **During 10 year  |
|             |                |                  | run**             |
+-------------+----------------+------------------+-------------------+
| ## Sole     | **180 ppm      | **100 % Helium   | **None**          |
| noid system | Helium**       | \< 1 min.**      |                   |
|             |                |                  |                   |
|             | **\[Away from  | **\[Away from    |                   |
|             | tubes\]**      | tubes\]**        |                   |
+-------------+----------------+------------------+-------------------+
| **VLPC      | **270 ppm      |                  | **None**          |
| system**    | Helium**       |                  |                   |
|             |                |                  |                   |
|             | **\[Away from  |                  |                   |
|             | tubes\]**      |                  |                   |
+-------------+----------------+------------------+-------------------+
|             | **10 ppm       |                  | **None**          |
|             | Helium**       |                  |                   |
|             |                |                  |                   |
|             | **\[4 to 6     |                  |                   |
|             | "B,C" layer    |                  |                   |
|             | tubes\]**      |                  |                   |
+-------------+----------------+------------------+-------------------+
|             |                | **1.3 % He       | **None**          |
|             |                | decaying to      |                   |
|             |                | \<100 ppm in 5   | **Lifetime at     |
|             |                | min.**           | 1.3% is 45 days.  |
|             |                |                  | Expect 1.3% for   |
|             |                | **\[By 10 to 20  | total 80 min.     |
|             |                | "B" layer        | over 10 year      |
|             |                | tubes\]**        | run**             |
+-------------+----------------+------------------+-------------------+
| **          | **Negligible   | **7 % He         | **None**          |
| Calorimeter | probability**  | decaying to      |                   |
| cold valve  |                | \<100 ppm in 30  | **Lifetime at 7%  |
| actuation   |                | minutes**        | is 8 days.**      |
| gas**       |                |                  |                   |
|             |                | **\[By 2 "A"     | **Expect to       |
|             |                | layer tubes\]**  | actuate cold      |
|             |                |                  | valve 2 to 4      |
|             |                |                  | times over 10 yr  |
|             |                |                  | run.**            |
+-------------+----------------+------------------+-------------------+
| **Tev       | **100 to 200   | **5 % He         | **None- Lifetime  |
| Magnet**    | ppm Helium**   | decaying to      | at 5%:**          |
|             |                | \<100 ppm in 25  |                   |
|             | **\[Away from  | minutes.**       | **Borosilicate    |
|             | tubes\]**      |                  | tubes, 11 days**  |
|             |                | **\[Magnet       |                   |
|             |                | rupture,         | **Quartz tubes,   |
|             |                | Envelopes D0     | 167 minutes**     |
|             |                | detector\]**     |                   |
|             |                |                  | **Expect maybe 1  |
|             |                |                  | discrete event    |
|             |                |                  | during entire     |
|             |                |                  | run.**            |
+-------------+----------------+------------------+-------------------+

**[Discussion and Background:]{.underline}**

Helium is present in the earth's atmosphere at about 5 parts per
million. (ref. Technology of liquid helium, NBS monograph 111). The
D-Zero detector uses helium for the cryogenic cooling of its
superconducting magnet and visible light photon counter (VLPC)
electronics chips. In addition, the tevatron accelerator has
superconducting magnets that use helium. Due to the possibility of leaks
or releases of helium from these helium lines and components, the
background helium level in the collision hall may exceed the natural
level of 5 ppm. This engineering note will quantify the probability and
level of helium background in the D-Zero detector.

The photomultiplier tubes used in the D-Zero detector are sensitive to
an elevated helium atmosphere. This is due to the permeation rate of
helium gas through the glass tube, into the vacuum space inside. It is
very important for the helium atmosphere surrounding the photomultiplier
tubes is known and controlled. If the level of helium in the vacuum tube
reaches a level above 5 ppm, then the photomuliplier tube may no longer
work as designed. The process is an irreversible one.

### Photomultiplier tube susceptibility

The time for the helium level in the photo tube to reach a certain level
by diffusion is given by[^1]:

Time =-tau\* (1-P~tube~/P~surroundings~) where: tau = 10^10^ seconds for
Borosilicate glass

= 10^9^ seconds for UV glass

= 10^8^ seconds for Quartz glass

This information is shown in the Table 1

**Table 1.** Time to reach 5 ppm for a sustained exposure

+----------------+-------------------+----------------+----------------+
|                |                   | #####          |                |
|                |                   |  Exposure Time |                |
+----------------+-------------------+----------------+----------------+
| [Sustained     | [Qu               | [UV            | [Borosilicat   |
| Helium         | artz]{.underline} | glas           | e]{.underline} |
| Exposur        |                   | s]{.underline} |                |
| e]{.underline} |                   |                |                |
+----------------+-------------------+----------------+----------------+
| 5 ppm          | infinite          | infinite       | infinite       |
+----------------+-------------------+----------------+----------------+
| 10 ppm         | 2.2 years         | 22 years       | 200 years      |
+----------------+-------------------+----------------+----------------+
| 100 ppm        | 59 days           | 1.6 years      | 16 years       |
+----------------+-------------------+----------------+----------------+
| 0.1%           | 6 days            | 58 days        | 1.6 years      |
+----------------+-------------------+----------------+----------------+
| 1 %            | 14 hours          | 6 days         | 58 days        |
+----------------+-------------------+----------------+----------------+
| 10 %           | 83 minutes        | 14 hours       | 6 days         |
+----------------+-------------------+----------------+----------------+
| 100 %          | 8.3 minutes       | 83 minutes     | 14 hours       |
+----------------+-------------------+----------------+----------------+

### 

### Quartz photomultiplier tubes are going to be used for the luminosity monitors. They will be located between the central calorimeter and end calorimeters surrounding the beam pipe. Note that their location is at least 5 meters away from any helium source. From Table 1 it is seen that the quartz photomultiplier tubes can tolerate a high level of concentration for a short time. A sustained low level concentration of only 10 ppm however, could cause a premature death of the tubes before the 5 to 7 year physics run is complete.

### 

### The muon trigger counters use Borosilicate photomultiplier tubes. These tubes are more widely distributed through out the D0 detector. They are mounted on the "A", "B", and "C" layers of the proportional drift tube chambers. These tubes are more hardy and can tolerate a reasonable elevated helium background.

### Helium dispersion behavior

A helium leak disperses into the surrounding air by diffusion and rises
upward due to its lesser density. To better understand qualitatively
what it happens, I can calculate some dimensionless parameters. First, I
assume the case of a discrete release of helium that mixes evenly with
the surrounding air into a 1 meter diameter sphere. Assume the
helium/air mix is 5 % helium, 95 % air.

The Grashoff number (Gr)[^2] is the ratio of the buoyancy forces to
viscous forces for the gas. It typically is calculated to understand
free convection heat transfer. A warm or cold surface induces flow by
changing the fluid density.

Gr=g\*Beta\*(Ts-Tinf)\*L\^3/mu\^2 where: g= acc. Due to gravity, Beta=
fluid expansion coeff.,

Ts=surface temp., Tinf=temp. far away,

> L=characteristic length, mu= viscosity

Beta = (1/RHO)\*(RHOinf-RHO)/(Tinf-T) where: RHOinf=fluid density far
away,

> RHO=fluid density of air/helium mix,
>
> T=Avg.,Fluid temp = (Ts+Tinf)/2

Substituting the second equation into the first, the temperatures cancel
out. By plugging in all the values, and using 1 meter for the
characteristic length, Gr= 4000. The buoyancy force is huge compared to
the viscous drag type forces on the fluid mix.

The Schmidt number (Sc) provides a measure of the relative effectiveness
of momentum and mass transport by diffusion in the velocity and
concentration boundary layers.[^3] It is the ratio of viscous forces and
mass diffusivities.

Sc= mu/D where: mu= viscosity, D = binary diffusion coefficient

The Binary diffusion coefficient for helium in air is not given in
reference 2. They are given for other gasses in air, including hydrogen,
which is probably similar to helium in diffusion. All the binary
diffusion coefficients are about the same order of magnitude, and
guessing the value to be the same as hydrogen, Sc=0.5. The viscous
transport and diffusion transport are the same order of magnitude.

The ratio of the buoyancy force to mass diffusivities can obtained by
multiplying the Grasshoff number by the Schmidt number. The result is
Gr\*Sc= 2000. This shows that the buoyancy force dominates the way the
helium moves away from the release sight. The buoyant transport is about
a 2000 times larger influence than the diffusion transport of the
helium. The helium will go straight up and make its way out of the
collision hall.

One can also calculate that the 1 meter sphere of 5 % helium and 95 %
air will have a net buoyancy force of 0.26 Newtons. Applying a=F/M, we
find that the acceleration on the helium sphere is 0.48 m/s\^2. It takes
about 2 seconds for the sphere to move upward 1 meter.

These calculations give one the intuitive sense that the helium will
rapidly rise vertically before it disperses outward horizontally.
Trapped helium in inverted pockets could possibly occur, but shouldn't
be a problem for the phototube installations.

# **Sources of helium in the D-Zero detector:**

1.  Liquid helium supply/returns for solenoid

2.  Lead flow returns from solenoid

3.  Relief valves from solenoid control dewar

4.  Liquid helium supply/returns for VLPC detector

5.  Cassette space gas helium volume

6.  Calorimeter cold valve actuation gas

7.  Tevatron magnets and tunnel

Each of the above sources will be elaborated on below. Specifically, I
will: a.) speculate method of the release, b.) describe the location,
c.) quantify the potential and amount of a helium release, d.) calculate
the helium concentration and duration of such a release. Quite a few
assumptions are made to arrive at hard numbers. The volume around the
leak is assumed to be ventilated at the rate of ¼ volume change per
minute. This is the approximately the same ratio as the collision hall
ventilation rate. Fans of 23,700 cfm (AHU-1 gives 19,200 cfm, EF-7 gives
4500 cfm) move air through the 100,000 cubic foot D0 detector. The
volume change is assumed to be with fresh air with no elevated
concentration of helium. This assumption is valid because the huge
volume of the collision hall dilutes virtually all the helium leaks to a
negligible level.

1.  [Liquid helium supply/returns for solenoid:]{.underline} A
    reasonable method of a release from theses lines would be through a
    failed o-ring leak at the u-tube bayonet fitting, a leaking trapped
    volume relief, a leaking tube fitting from a pressure tap to
    transmitter line, valve packing leak etc. All these potential types
    of leaks occur at the control dewar location positioned outside the
    detector at an elevation about 12.5 feet above the beam line. There
    are no photo tubes mounted above the location. The nearest photo
    tubes are 2 to 3 feet to the north and west of the location. The
    likelihood of such a leak is say 25 items \* (3E-6 failures/hr)
    (8766 hrs/yr) = 0.7 leaks per year. The total leak rate would be a
    maximum of 1 cc/sec air = 0.005 scfm helium. (Note that a leak
    detectable by snoop is 1/1000^th^ of this = 0.001 atm-cc/sec air).
    For the sake of a number, assume the helium is distributed through a
    spherical volume with 3 foot radius. The resultant helium background
    would be around 180 ppm. The concentration level should reduce as
    cubic function of the distance from the source. The duration of such
    a release could be for the whole run since the leak may not be
    noticed or discovered. Even though the probability is that one such
    leak would occur every year and a half, the total leak rate assumed
    is rather large and should account for any combination of multiple
    leaks that may occur during the run.

+-----------------------------------------------------------------------+
| **180 ppm Helium**                                                    |
|                                                                       |
| **\[Away from tubes\]**                                               |
+-----------------------------------------------------------------------+

2.  [Lead flow returns from solenoid:]{.underline} The method and
    location of a leak from these items is similar to the solenoid
    supply lines above. The elevation of such a leak is a few feet
    higher, within 5 feet of the top of the detector. There are going to
    be 6 potential leak sites all enclosed in the lead flow purge box.
    The GN2 purge box would dilute any such leak by about 0.5 scfm
    purge/0.005 scfm helium = 100 before it's release out of the box.
    The elevated helium concentrations are 100 times less than those
    calculated for source number 1. That is (5 ppm (natural
    background) + 6 ppm=) 11 ppm at 2 feet away and (5 ppm (natural
    background) + 2 ppm=) 7 ppm at 3 feet away.

+-----------------------------------------------------------------------+
| **Negligible ppm**                                                    |
|                                                                       |
| **\[Away from tubes\]**                                               |
+-----------------------------------------------------------------------+

3.  [Relief valves from solenoid control dewar]{.underline}: The
    solenoid has relief valves that protect the process lines and helium
    subcooler vessel. The cause of a relief discharge could be a quench
    or an operational upset. The location of the discharge and elevated
    helium atmosphere is the control dewar location described in the
    previous cases. It's hard to estimate how often a release could
    happen, in the operational test of the magnet at Toshiba the relief
    valves did not come close to having to open from a forced quench of
    the magnet. For a rough guess, say it might occur 4 times a year.
    The rate of release is large 616 cfm helium, for a short duration,
    say 5 seconds at most, for a release of about 50 scf helium
    (equivalent to 2 liquid liters of helium). The local concentration
    would initially be high, approximately 100 % up to 3 feet from the
    relief valve. Modeling the helium as a sphere, the sphere would rise
    above and away from the detector in a matter of seconds. Any such
    releases from the relief valves would be discrete short term
    exposures of helium to the tubes.

+-----------------------------------------------------------------------+
| **100 % Helium \< 1 min.**                                            |
|                                                                       |
| **\[Away from tubes\]**                                               |
+-----------------------------------------------------------------------+

4.  [Liquid helium supply/returns for VLPC detector:]{.underline} These
    lines connect via u-tubes in the same area as the solenoid control
    dewar. There are 6 bayonets and 6 trapped volume relief valves at
    that location. The conservative failure rate of the bayonets and
    relief valves is about 0.3 failures per year. A leak rate of 0.005
    scfm helium is reasonable. The duration of such a leak would
    probably be for the duration of the run. The maximum local
    concentration at the end of 5 years above the bayonet feed can could
    be (5 yrs)(0.3/yr)(180 ppm)= 270 ppm. This location is not in the
    area of any photo tubes.

+-----------------------------------------------------------------------+
| **270 ppm Helium**                                                    |
|                                                                       |
| **\[Away from tubes\]**                                               |
+-----------------------------------------------------------------------+

The other leak sources are the stems of two control valves located in a
valve box in the center-east section of the detector platform. These
stems are bellow sealed and each have a failure rate of about
(1E-8/hr)\*(8677 hrs/yr)=1.7E-4 per year. The valve box location is
probably within 10 feet of a "B" or "C" layer photo tube. The failure
rate is low enough that it can be neglected. If it did fail, the mixing
and distances involved would probably cause a maximum helium
concentration of about 80 ppm at the closest photo tube location. The
helium concentration would probably dilute by the distance from the
source cubed. So photo tubes 20 feet away would see at most 10 ppm above
the normal atmospheric concentration.

+-----------------------------------------------------------------------+
| **10 ppm Helium**                                                     |
|                                                                       |
| **\[4 to 6 "B,C" layer tubes\]**                                      |
+-----------------------------------------------------------------------+

5.  [Cassette space gas helium volume:]{.underline} The cassette space
    volume is located in the center of the detector platform. The
    cassette space is a stagnant volume that surrounds the cold end of
    each of the 102 VLPC cassettes. Each VLPC cassette has a gasket and
    silicone potting at the warm optical fiber/flex circuit bulkhead.
    I'll estimate the leak rate for a cassette bulkhead to be 1E-2
    atm-cc/sec helium= 2E-5 cfm helium. Multiplied by the 100 cassettes,
    then the total steady state leak rate is going to be 0.002 cfm
    distributed over the 1.5 ft x 12 ft long surface area of the
    cryostats. The center section of the platform is ventilated with
    fans at a rate of 2080 cfm and has a volume of about 1600 cf. The
    raised helium concentration from the cassette leaks is on the order
    of 1 or 2 ppm.

+-----------------------------------------------------------------------+
| **Negligible ppm**                                                    |
|                                                                       |
| **\[By 10 to 20 "B" layer tubes\]**                                   |
+-----------------------------------------------------------------------+

> There are going to be low pressure relief valves protecting the
> cassette space. These will relieve pressure generated from a warm up
> of the cassette space. These relief valves are going to have their
> outlets piped into the argon spill duct which is located not more than
> 10 feet away. The spill duct has continuous ventilation out of the
> detector area.
>
> A cassette change operation would also release helium gas. A cassette
> change would occur 2 times per year at most. Operational spares are
> included as a subset of the total 102 cassette installation. During a
> change out one probably would keep a positive helium supply to the
> cassette space to prevent back streaming of air and moisture into the
> cassette space which could be cold. In between the actual removal of
> the cassette and blanking off the hole again, helium would escape out
> of the cassette slot for 1 to 2 minutes. I estimate 30 scf of helium
> is released during this operation. The elevated helium background in
> the center section of the platform could be as high as 1.25% =12,500
> ppm helium for a couple of minutes. The concentration would then
> decrease exponentially thereafter.
>
> ![](media/image1.wmf)

+-----------------------------------------------------------------------+
| **1.3% He decaying to \<100 ppm in 5 min.**                           |
|                                                                       |
| **\[By 10 to 20 "B" layer tubes\]**                                   |
+-----------------------------------------------------------------------+

6.  Calorimeter cold valve actuation gas: The cold valves are fed by ¼"
    tubing lines that run from the cryo corner area (SE corner of
    platform) up the cryobridge and to the tops of the three
    calorimeters. The tubing for the most part is continuous with some
    joints. There are muon chambers and counters within a few feet of
    the tubing run. The probability of a leak is around (10
    joints)(1E-8/hr)(8766 hr/yr)=0.00087 per year or about 1 in a 1000
    odds. The maximum leak that could reasonably occur is around 0.005
    scfm. This leak could cause an elevated helium atmosphere of 500 ppm
    at the closest photo tube should a leak occur. Another release is
    due to the actuation of the cold valve. The solenoid that applies
    helium to the cold valve releases a slight burp when energized. The
    manufacturer says there is a slight leakage, so I'll interpret that
    to be 1% of the full flow Cv=0.09 (orifice of 1/16"). The equivalent
    leak rate is 0.9 cfm. This is a momentary 5 second puff that could
    cause a local atmosphere of 7% helium within a foot of the solenoid.
    This would rapidly dilute away due to the density difference between
    the helium and air regardless of whether there was a trapped pocket
    above the location or not.

+-----------------------------------------------------------------------+
| **7% He decaying to \<100 ppm in 30 minutes**                         |
|                                                                       |
| **\[By 2 "A" layer tubes\]**                                          |
+-----------------------------------------------------------------------+

7.  Tevatron magnets and the tunnel: This is a hard source to quantify.
    The components are located on the north and south ends of the
    collision hall and would impact the outer most layer of counters on
    the north and south faces of the detector. The magnets and tunnel
    probably would have a steady state leak rate and probability not too
    different from the solenoid control dewar components, sources 1
    through 4. The ODH analysis (conservative) lists a maximum leak rate
    from a powered low beta quad magnet at 1898 scfm. The probability of
    such a failure is 2E-6/hr = 1 in 60 chance per year (also
    conservative). The circulating ventilation rate (non fresh make-up)
    for the collision hall is 24,000 cfm and the volume of the collision
    hall is about 100,000 cf. Just to get a number, assume the failure
    occurs and the release lasts for 3 minutes. In that time, about 5700
    cf of helium would be released into 100,000 cf of air. The helium
    concentration could be as high as 5 to 7% initially. The gas helium
    would escape out the top of the collision hall, and the large ODH
    ventilation fans would be kicked on mixing and diluting the
    concentration from there. The ventilation rate during such an event
    would be at least ¼ volume change per minute.

+-----------------------------------------------------------------------+
| ![](media/image2.wmf)**5% He decaying to \<100 ppm in 25 minutes.**   |
|                                                                       |
| **\[Magnet rupture, Envelopes D0 detector\]**                         |
+-----------------------------------------------------------------------+

[^1]: E-mail communication from Rich Partridge, Brown University,
    referenced from Hamamatsu photomultiplier data book. Tau is
    representative, not exact as D0 is not using Hamamatsu photo tubes.

[^2]: ^2^ Incropera and Dewitt, Fundamentals of heat and mass transfer,
    2^nd^ ed., 1985.

[^3]: Incropera and Dewitt, Fundamentals of heat and mass transfer,
    2^nd^ ed., 1985.