High Gradient Lithium Lens

December 19, 2002

J. Morgan

# Motivation

![](media/image1.wmf){width="6.0in" height="5.944444444444445in"}The
antiproton source incorporates a lithium lens to greatly improve the
transmission efficiency of antiprotons into the Debuncher ring. A
lithium lens is ideally suited for capturing the highly divergent
antiproton beam emanating from the target into a phase space that can be
transported through a beamline with magnets of conventional dimensions.
The lens has a large axial current passing through a solid lithium
cylinder that produces a strong magnet field approximately proportional
to the radius. The lens also has the advantage that it focuses in both
transverse planes. The design gradient of the 1 cm. radius lithium lens
was 1,000 T/m (10 Tesla surface field). However, operational lenses have
not been able to sustain the design gradient for enough pulses to be
practical. Lenses at the design gradient have failed within days or
weeks due to mechanical failures of the titanium tube that contains the
lithium. Peak stresses in the titanium rise rapidly as the electrical
current and Ohmic heating are increased. Running lenses at reduced
gradient has allowed them to survive for an acceptable length of time,
millions of pulses and an operational life of greater than 6 months. The
penalty for lowering the gradient is less antiproton yield due to the
reduction in focusing strength. The operational gradient of the lithium
lens is 745 T/m, to achieve the compromise between service life and
performance.

Beam models and measurements indicate that the antiproton yield can be
increased by running the lithium lens at an increased gradient. Figure 1
shows the predicted relationship between antiproton yield and lithium
lens gradient as a function of transverse acceptance. Two sets of
measurements are also included that are in reasonably good agreement
with the model. The ideal gradient is dependent on the optics and
acceptance of the AP-2 line, but in most cases is around the design of
1,000 T/m. Operating at 1,000 T/m instead of 745 T/m is expected to
increase the antiproton yield by about 10% with the present AP-2 and
Debuncher acceptance, and up to 17% after the acceptance is doubled.

## Goals

The manufacturing process for a lithium lens is sufficiently complex and
lengthy so that the rate of production has roughly equaled the rate of
failure, even operating well below the design gradient. Table 1 provides
the observed relationship between lens gradient and the expected
lifetime. The number of pulses to failure is based on subjective
estimates due to the small number of lenses that have been used and
assumes no manufacturing flaws.

The high gradient lithium lens project was undertaken in order to
increase the operational gradient to 1,000 T/m with a 1 cm. radius lens
and achieve a lifetime of 10,000,000 pulses. Even if this goal is not
completely achieved, any increase in gradient from the 745 T/m level
presently used will produce a partial increase in antiproton yield. To
achieve this goal, there have been three main categories of effort.

> ●A collaboration between Fermilab and BINP in Novosibirsk was
> initiated in 1997 to develop a liquid lithium lens. The perceived
> advantage of a liquid lithium lens is that the stresses are reduced
> due to the fluid characteristics of the liquid lithium and the use of
> buffer volumes. Cooling water would no longer be necessary, as heat
> deposited in the lithium conductor would help keep the lithium in the
> liquid state. The support systems for a liquid lithium lens are
> technically difficult to design and operate reliably.
>
> ●Design enhancements to the existing lithium lens to improve the
> longevity of the lenses. To be successful, research is required into
> the material properties of lithium and titanium, autopsies are to be
> performed on lenses that failed during operation and more
> sophisticated mechanical modeling needs to be developed. Quality
> control issues must also be examined with an emphasis on the handling
> and acid etching of the inner septum tube and the lithium fill
> process.
>
> ●Research and development of a new design solid lithium lens utilizing
> diffusion bonding, eliminating the electron beam welds on the present
> lens. Alternative titanium alloys can be considered because good
> welding characteristics would not be required. The new lens body would
> be made entirely of titanium and requires major changes in the
> geometry of the lens. The diffusion bonding technique achieves more
> complete bonding with more uniform microstructure. A lens of this
> design also has the advantage that the fabrication of the lens body
> assembly can be made quickly and less expensively by an outside
> vendor.

## Status

#  Liquid lithium lens

The liquid lithium lens project was effectively terminated during 2002.
The challenges in producing a reliable liquid lithium lens appear to be
too great to overcome within the time scale of Collider run II. Pulse
tests on the prototype liquid lithium lenses have not been promising,
with septum failures occurring at low gradients and small numbers of
pulses.

#  Solid lithium lens improvements

Past lens failures have been analyzed with a combination of a Finite
Element Analysis (FEA) of the lithium lens and autopsies of the failed
lenses. Results of the FEA analysis to date suggest that peak stresses
in the operational lens should be significantly below the fatigue
strength of the Ti 6Al 4V septum. If the model is accurate, this would
suggest that cracks are initiated by another mechanism. Possible sources
of crack initiation would be liquid metal embrittlement during the lens
fill, acid etching during lens fabrication and hydrogen embrittlement.

Five lenses that failed in service have had their lithium removed and
are in various stages of analysis. One of the lenses, #16, did not have
a septum failure and was instead removed from service due to a water
leak. The other lenses, #17, 18, 20 and 21, developed fractures in the
septum that separates the lithium conductor from the cooling water. The
analysis process involves sectioning of the lenses, and examination with
both an optical microscope and a scanning electron microscope. The
septum is examined at various points near the failure area as well as in
the "good" material. Lens #16 is being examined to find whether cracks
had begun to develop in this lens after several million pulses.
Preliminary results of the autopsies show that there are signs of small
cracks developing in the septum away from the main fracture area,
suggesting that cracking had been initiated prior to pulsing the lens.

Due to concerns about cracks developing during the fabrication of the
lens, quality control has been improved in the solid lens fabrication.
Two new lenses, #27 and #28, were completed during the year and included
most of these improvements. Oxidation to the inner septum during the
welding process was greatly reduced by developing protective shields.
The acid etching of the inner septum was performed more uniformly and
with a weaker acid to reduce the risk of crack development. The lithium
filling process was completely revamped to greatly reduce the error in
measured pre-load and reduce the length of time that lithium is molten
during the fill process. Lens #27 incorporated low-ELI titanium, which
is considered superior in this application.

Measurements have been made to better understand the mechanical
properties of lithium and titanium. Endurance tests with Ti 6Al 4V have
been made with several geometries and joining techniques to duplicate
conditions in the existing solid lens as well as the diffusion bonded
lens. Tests have been made to investigate possible liquid metal
corrosion during the filling process by dipping stressed titanium
samples into liquid lithium. An instrumented titanium tube has been
filled with lithium to measure rates of mechanical creep. Several
fundamental measurements of the mechanical properties of lithium have
been required due to the lack of available experimental data.

Mechanical models of the lens suggest that increasing the wall thickness
of the inner septum can reduce stresses. The present design has a 1 mm.
septum wall thickness, which provides some flexibility and good heat
transfer to the cooling water. Models suggest that increasing the
thickness by approximately 50% will significantly reduce peak stresses
while maintaining acceptable heat transfer rates. The reduced
flexibility of the thicker tube will require additional pre-load to be
applied during the filling process to ensue good lithium to titanium
contact during the current pulse. Another geometry change being
contemplated is a longer septum, 18 cm. instead of 15 cm., to increase
the integrated field by 20%. Ideally, the lens would be as strong and
short as possible to minimize absorption in the lithium and reduce
aberrations. A longer lens would only be built if the planned
improvements failed to produce a reliable high gradient lens. Both the
thicker lens and longer length lens can be made by making minor
modifications to the existing lens design.

#  New design solid lithium lens

The first prototype diffusion bonded lithium lens is in the process of
being completed. The titanium body was successfully bonded, and
machining is being completed so the lens can be filled. The lens will
require a larger lithium preload pressure due to the thicker inner
septum that is less flexible. Prototype lens #1 has a smaller diameter
conductor, and is in large part a "proof of principal" for a diffusion
bonded lens. During the testing process, the current will be gradually
increased until a surface field of 10 Tesla is achieved. If the lens is
able to sustain prolonged pulsing at the elevated gradient, fabrication
of the second prototype lens will proceed. Prototype lens #1 will be
tested to failure and analyzed for the failure mechanism. If the lens
fails prematurely, the prototype design will be reassessed and either
corrected or terminated.

Prototype lens #2 has gone through the design phase and has incorporated
significant changes from the first prototype. The diffusion bonded joint
at the center of the inner septum has been eliminated. The lithium
conductor radius is increased to 1 cm, which is the radius of the
operational lens. Changes have also been made to the water passages to
accommodate the larger lithium conductor. Fabrication of the second lens
will be delayed until testing of the first prototype has been completed
to ensure there are no unexpected design flaws.

## Plan

One more lens, #22, is scheduled for lithium removal and autopsy in FY
2003. The lens had a septum breach in September 2001 and was removed
from service. The lens is very radioactive but has cooled significantly
over the last 15+ months. This lens is particularly interesting because
it accumulated the most pulses during its service life (\>9.2 million)
and did not fail during pulsing. The failure region should be unusually
pristine since it would not have experienced the usual arcing in the
failure region from cooling water entering the lithium conductor and
forming lithium hydroxide. In addition, analysis of the other autopsied
lenses will be completed in FY 2003.

The FEA model will continue to be refined and expanded in FY 2003.
Models will be developed for the existing operational lens, the
prototype lenses and the thicker septum lens. Efforts will continue to
develop a model that accurately simulates failure mechanisms in the
lithium lenses to facilitate design changes.

The top priority for the first half of FY 2003 is the completion of
prototype lens #1 so that it can be tested. The diffusion bonded lens
has the longest lead-time of the various design options. The test of
prototype lens #1 will be very valuable in evaluating the future of this
design and will be used to identify design improvements to prototype
lens #2. It is anticipated that fabrication of prototype lens #2 will
begin during the second half of FY 2003, with testing beginning in the
second quarter of FY 2004. Prototype lens #2 will probably be tested
both on the test stand and with beam in the target vault.

During the second quarter of FY 2003, Lens #27 will be put into service.
After about a month of operation at a gradient of 745 T/m, the gradient
will be increased to 820 T/m and pulsed to failure. Since lens #27
incorporates all of the quality control improvements identified over the
past two years, this should help quantify if they will improve the
longevity of lenses. Experience with past lenses suggest that the
service life will be greatly shortened (Table 1) by running at 820 T/m
if the quality control changes did not improve the durability of the
lens.

Construction of two new lenses, #29 and 30, will be initiated late in
the second quarter of FY 2003. These lenses will incorporate a thicker
inner septum (approximately 1.5 mm instead of 1.0 mm) to reduce peak
stresses. However, the thicker septum will conduct more current and
transmit heat to the cooling water more slowly. These two drawbacks do
not appear to be a serious problem and models suggest that the lens
could be run at 5-10% higher gradient with the same stresses as the
thinner septum presently used. These lenses would be tested early in FY
2004 and could be used operationally soon afterward.

Presently, design and fabrication of the longer 18 cm lens is not being
actively pursued. Models suggest a modest (2-4%) gain in antiproton
yield can be expected from this style lens. However, the design is
relatively easy to implement and much of the preliminary work has
already been done. A lens of this design would provide useful data to
compare to the beam models while providing a small boost in antiproton
yield. A lens of this design may be produced in FY 2004, depending on
progress with the other alternative designs and aperture improvements in
AP-2 and the Debuncher.