Final Focus Shielding Designs for

Modern Heavy-Ion Fusion Power Plant Designs

J. F. Latkowski and W. R. Meier

*Lawrence Livermore National Laboratory, P.O. Box 808, Mailstop L-446,
Livermore, California 94550 USA*

**Abstract**

Recent work in heavy-ion fusion accelerators and final focusing systems
shows a trend towards less current per beam, and thus, a greater number
of beams. Final focusing magnets are susceptible to nuclear heating,
radiation damage, and neutron activation. The trend towards more beams,
however, means that there can be less shielding for each magnet.
Excessive levels of nuclear heating may lead to magnet quench or an
intolerable recirculating power for magnet cooling. High levels of
radiation damage may result in short magnet lifetimes and low
reliability. Finally, neutron activation of the magnet components may
lead to difficulties in maintenance, recycling, and waste disposal. The
present work expands upon previous, three-dimensional magnet shielding
calculations for a modified version of the HYLIFE-II IFE power plant
design. We present key magnet results as a function of the number of
beams.

*Keywords:* Inertial fusion energy; Magnet shielding; Final focus

**1. Introduction**

Final focusing magnets for heavy-ion fusion power plant designs must
survive exposure to intense fluxes of neutrons and γ-rays. If not
sufficiently shielded, superconducting final focusing magnets may be
subject to quench. Normal and superconducting magnets will need to be
actively cooled due to energy deposition by neutrons and γ-rays, and
they will need a high resistance to radiation damage. Finally, neutron
activation, which can lead to maintenance and waste management
difficulties may be a significant issue for some magnet materials.

Previous power plant designs have been able to effectively shield the
final focusing magnets due to the small number of beams (12-20) that
allowed large shielding thicknesses (30-40 cm) on the inner bore of each
magnet \[1,2\]. More recent work, however, has reduced the current per
beam at the cost of a greater number of beams and less space per beam
for magnet shielding \[3,4\]. Here, we utilize a self-consistent,
integrated source-to-target model for induction linear accelerator
drivers to determine the beam and magnetic parameters at the final focus
magnets. We use this model to study the trade-offs between magnet
shielding and the number of beams for a modified version of the
HYLIFE-II power plant design \[5\].

**2. Description of IBEAM final focus model**

The IBEAM (Ion Beams for Energy Applications Model) model has been used
to establish parameters for four point design final focusing arrays.
Each case assumes target illumination from two arrays of 6 × 6, 8 × 8,
10 × 10, or 12 × 12 beams. The model begins with calculation of the beam
spot size on target, r~s~, which is calculated as:

$r_{s} = \sqrt{r_{\text{se}}^{2} + r_{\text{ca}}^{2} + r_{\text{ga}}^{2} + r_{\text{aim}}^{2}}$
(1)

Where spot size radius contributions are:

r~se~ = coupled space charge and emittance effects

r~ca~ = chromatic aberrations

r~ga~ = geometric aberrations

r~aim~ = aiming

The driver considered here is required to deliver 3.3 MJ to the target
with an average spot size on target of 1.7 mm. This total beam energy
can be divided into any number of beams, with economics considerations
favoring a rather large number of beams (\> 100 depending on the ion
used) \[6\]. The example used in this study was for cesium ions (A =
133). The space charge and emittance term is found by solving the beam
envelope equation for the spot size consistent with the focus half
angle, θ. The normalized emittance that enters the equation depends on
the emittance of the source (which decreases with increasing number of
beam) and how that emittance grows between the source and final focus
system. We assume a total growth factor of seven, but this is the
subject of ongoing research in the heavy ion fusion program. Space
charge also decreases with increasing number of beams as the total
required charge is divided into a larger number of beams. Space charge
effects are further diminished by neutralizing the beams by 99% as they
leave the final focus magnets. The chromatic aberration contribution is
proportional to the momentum spread (which is held constant here), the
final focus length, L~f~ (also constant at 5.5 m), and the final focus
half angle, θ, which is one of the design variables we consider.
Geometric aberrations go as (L~f~θ)^3^, and aiming is assumed to be a
constant 200 μm. Figure 1 shows the contribution to spot size as a
function of θ for a 72-beam case.

To investigate the effect of smaller beam port sizes, we examined a
range of cases with larger numbers of beams. In each case, the focus
half angle yielding the minimum spot size on target was used to
calculate the beam port size. Key parameters for the cases considered
are given in Table 1. The maximum beam radius is \~ 1.3 times the
average beam radius, which is simply L~f~ × θ. The bore inner radius is
1.25 times the maximum beam radius plus a 0.5 cm additional clearance
allowance. The winding inner radius is at R~bore~ plus 7 cm---2 cm for
the beam tube wall, insulation and cooling combined plus 5 cm for
shielding . The winding thickness depends on the B-field as does the
thickness of the steel collar. Windings are assumed to be constructed
from 40% Nb-Ti superconductor, 40% Cu, and 20% liquid helium, on a
volumetric basis.

**3. Transport models**

The radial builds specified in Table 1 have been used in neutron and
γ-ray transport models. These calculations yield particle spectra and
energy deposition in each region of each magnet. With this information,
power loadings, cooling power, radiation damage, and neutron activation
may be calculated.

HYLIFE-II includes a 60-cm-thick Flibe pocket and an additional 50 cm of
Flibe within the blanket \[6\]. The first wall and blanket structure
consists of four stainless steel type 304 (SS304) shells. For the
purposes of this exercise, only the last focusing magnet has been
modeled. Figure 2 is a plot of the geometry for the 288-beam case.
Visible are the Flibe pocket with penetrations, the chamber and blankets
shells, the first wall shielding packets that surround each array of
beams, and the magnets themselves. The top portion of the geometry has
been removed to allow one to see inside the chamber. Similar models have
been used for the 72-, 128-, and 200-beam cases. Neutron and γ-ray
transport calculations have been completed using the TART98 Monte Carlo
code \[7\]. A total of 200 million particles were transported for each
case. Neutron activation calculations have been performed with the
ACAB98 radionuclide generation/depletion code using the FENDL/A-2.0
activation cross section library \[8,9\].

**4. Results**

Results from TART98 are generated on a per-source-neutron basis. We have
normalized these results according to the baseline operational
parameters for the HYLIFE-II design. Specifically, we assume operation
at 6.4 Hz with a target yield of 350 MJ for a total fusion power of 2240
MW \[6\]. Prompt heating results are presented on a per-shot basis.
These results are used to determine whether or not quenching is a
concern for the superconducting coils.

Cooling requirements are for steady-state operation, including
radioactive afterheat from neutron-activated magnet components. We
assume cooling efficiencies as a function of the operational
temperature: 50% for water-cooled regions, 5% for liquid-nitrogen-cooled
regions, and 0.5% for liquid-helium-cooled regions. Using these
efficiencies, we calculate the total recirculating power that would be
needed to cool the final set of magnets. If magnet shielding is not
adequate, the magnet cooling power may represent an unacceptable loss of
revenue.

Radiation damage from neutrons and γ-rays is presented for the magnet
coils. These dose rates would apply to the superconducting coils, the Cu
stabilizer, and any insulating materials. High dose rates may
necessitate frequent maintenance and/or replacement of final focusing
magnets. This may cause not only an economic penalty, but it also may be
a significant source of waste \[10\]. Therefore, we present neutron
activation results for the key major magnet subcomponents.

*4.1 Magnet heating and cooling*

If sufficiently high, prompt heating of the magnet coils could raise the
superconducting material above its critical temperature and cause it to
quench. For Nb-Ti superconductors, an energy deposition of 50-100 mJ/cc
is tolerable \[11\]. None of the cases analyzed for this work appears to
have a problem with magnet quench. Prompt heating results range from a
low of 0.8 mJ/cc in the 288-beam case to a high of 1.2 mJ/cc in the
72-beam case. Given that the designs have not been optimized to reduce
the heat loading on the coils, it seems unlikely that this is a serious
concern. Figure 3 shows the neutron and γ-ray spectra in the magnet
coils for the 72-beam case. These spectra are typical of the other cases
with the γ-ray spectrum peaking at \~ 100 keV.

The recirculating power that would be needed to cool the array of
magnets has been calculated for each case. Our results only include the
final array of magnets, and thus, some particles that scatter from the
next set of magnets have been neglected. Previous work found this to be
a 10-15% effect, so we increase our results by 15% \[10\]. Previous work
also found that the last magnet only accounted for 19-32% of the total
recirculating power \[10\]. Using this, we estimate the total cooling
power needed for all magnets and shielding material. Averaged over a
magnet, γ-rays are responsible for 85-90% of the energy deposition.

The cooling powers, shown in Table 2, also include contributions from
radioactive afterheat of the various magnet subcomponents (due to
neutron activation and subsequent radioactive decay). In each case,
afterheat is only contributes \~ 3% to the total cooling power. The
cooling required due to afterheat is dominated by the tungsten shielding
and the superconducting coil and stabilizer.

As indicated in the table, the recirculating power rises with the number
of beams from \~ 15 MW~e~ for the 72-beam case up to \~ 20 MW~e~ for the
288-beam case. While this is certainly not negligible at \~ 2% of the
electrical output of the power plant, it is for a design that has not
been optimized, so it can be reduced and is probably not a significant
issue.

*4.2 Magnet dose and lifetime for base cases*

The maximum dose and/or particle fluence that insulators,
superconductors, and stabilizers can withstand is not certain. Data for
fusion-relevant irradiations is sparse. Sawan et al. reported a lifetime
dose limit of 50 MGy (5 × 10^9^ rad) for epoxy electrical insulators
\[1\]. Other organic insulators are even less radiation resistant. Other
work has reported a disturbing result---the resistivity of copper
increased by 2.5% at a neutron fluence of only 2 × 10^17^ n/cm^2^
\[12\]. This can, of course, be circumvented through operation at a
lower current density, but this increases the radial build of the
magnets, and thus, the half-angle of the beams to the target.

Hahn et al. reported that Nb~3~Sn irradiated to a fluence of 2 × 10^18^
n/cm^2^ showed a 3 K drop in the critical temperature and a 2× reduction
in the critical current density \[13\]. In a review paper, Sawan and
Walstrom conclude that Nb-Ti can be annealed with 70% recovery after a
fast neutron (E~n~ ≥ 0.1 MeV) fluence of 3 × 10^18^ n/cm^2^ \[14\]. This
implies an end-of-life fluence limit of 10^19^ n/cm^2^. They report a
20% drop in the critical current of Nb~3~Sn after a fluence of 2 ×
10^19^ n/cm^2^ \[14\].

We adopt the 50 MGy value for the epoxy insulators. Additionally, we
assume a total fast neutron fluence limit of 10^19^ n/cm^2^ for the
superconductors and stabilizer. This assumption needs to be validated
with additional irradiations and analysis. Table 3 summarizes the dose,
fast neutron fluence, and estimated magnet lifetime results as a
function of the number of beams.

In all cases, the fast neutron fluence is the limiting factor on the
magnet lifetime. Based upon a fast neutron fluence limit of 10^19^
n/cm^2^, the magnet lifetimes range from 0.6-1.0 years. If a total dose
to the magnet coils, stabilizers, and insulators of 50 MGy is the
limiting factor, then the lifetimes would range from 1.3-2.0 years. In
either case, the magnet lifetime is, within a factor of two, only 1
year. (Note: Since the original presentation of this material,
additional work has been completed for the 72-beam case. This work
implements multiple shielding techniques and is able to extend the
estimated magnet lifetime to more than the expected power plant lifetime
of 30 full-power-years. This subsequent work will be presented at the
Fourteenth Topical Meeting on the Technology of Fusion Energy in Park
City, Utah in October 2000.)

*4.3 Neutron activation for base cases*

Neutron activation calculations have been carried out using the
estimated magnet lifetimes based upon a fast neutron fluence limit of
10^19^ n/cm^2^ (lower end of the ranges shown in Table 3). In all cases,
the Nb-Ti portion of the coils is problematic in that it is a source of
^94^Nb, a long-lived radionuclide. While a waste disposal rating (WDR)
less than unity is desirable, the base cases have WDR values ranging
from 6.1 for the 72-beam case to 7.7 for the 288-beam case. None of
these coils would qualify for disposal via shallow land burial. The
gradual increase in the WDR is primarily due to the increased lifetime
for the cases with a larger number of beams. Figure 4 shows the neutron
spectrum in the coils for the 72- and 288-beam cases.

Although none of the coils would qualify for disposal via shallow land
burial, all appear to qualify for remote recycling. After 50 years of
decay time following the irradiation, the contact dose rates range from
a low of 2.9 mSv/h (290 mrem/h) for the 72-beam case to 3.6 mSv/hr for
the 288-beam case. Typically, remote recycling is considered possible
for contact dose rates ≤ 100 mSv/h. The magnets would not qualify for
hands-on recycling, however, due to its limit of only 25 μSv/h. The
contact dose rates are all dominated by ^94^Nb, which is produced
primarily at neutron energies of less than 1 eV (^93^Nb is a classic 1/v
absorber) and at the resonances of the ^93^Nb(n,γ)^94^Nb and
^93^Nb(n,γ)^94m^Nb reactions (0.1-1 keV). Future work may seek to reduce
these reaction rates by adding materials with competing reactions in
these energy ranges (e.g., boron has a large absorption cross section
over both of these energy ranges).

*4.4 Results for enhanced shielding case*

The short estimated magnet lifetimes shown in Table 3 prompted the
creation of an additional case. While the four base case designs all
included 5 cm of tungsten shielding, this shielding was increased to 10
cm for a new version of the 72-beam case. Table 4 compares the radial
build and magnet properties of the enhanced, 72-beam case with the
72-beam base case. Due to the increased shielding, the outer radius of
each magnet increases from 15.1 to 21.7 cm, and thus, the half-angle of
the magnet array increases from 11.0 to 15.6 degrees. With the
additional shielding, the array half-angle is slightly larger than that
for the 200-beam base case. Recent target designs assume half-angles of
12.0 degrees for the main pulse beams, so additional work is needed to
extend target designs to larger angles \[15\].

Increasing the shielding thickness from 5 to 10 cm not only pushes the
inner radius of the coil out farther, but the need for a higher magnetic
field results in a substantially thicker coil and banding. As a result,
the coil and banding masses increase by 2.6× and 3.6×, respectively. Due
to the increased masses, cooling requirements also increase relative to
the 72-beam base case. The total recirculating power needed for cooling
the final magnet increases from 3.1 to 3.9 MW~e~, and the estimated
total cooling power is 12-21 MW~e~ versus 11-19 MW~e~ for the base case.
This increase is quite minor.

The total dose rate to the coils falls by 2.2×---from 39 MGy/y to only
18 MGy/y. The fast neutron fluence falls from 1.7 × 10^19^ n/cm^2^-y to
7.5 × 10^18^ n/cm^2^-y. Based upon these values, the magnet lifetime is
estimated as 1.3-2.8 years compared with the 0.6-1.3 years for the case
with only 5 cm of shielding.

The neutron activation of the magnet coil increases by about 30% due to
the softened neutron spectrum. The dominant long-lived radionuclide is
^94^Nb, which is produced predominantly via low-energy neutrons.
Nevertheless, the magnet coils would still qualify for remote recycling
as the contact dose rate would be only 3.7 mSv/h at a time of 50 years
after irradiation.

If we assume that increasing the shielding thickness from 5 to 10 cm
would have a similar effect for the 288-beam case, then we would predict
a magnet lifetime of 2.2-4.4 years. Of course, this would come with a
half-angle of 26.2° for the magnet array. Such a large half-angle is
incompatible with current target designs.

**5. Conclusions and future work**

While previous work considered drivers with only 12-20 beams and could
allocate 30-40 cm of shielding per beam, recent studies push designs
towards a greater number of beams to achieve substantial savings in the
cost of the accelerator. Increasing the number of beams, however, leaves
less room for radiation shielding, and thus, nuclear heating, radiation
damage, and neutron activation may be a concern. To address this issue,
we have investigated the shielding characteristics of the final focusing
magnets using a self-consistent source-to-target model, which includes
the final focusing parameters and only 5 cm of shielding for each
magnet.

Our results indicate that the damage rate to the sensitive
superconducting coils, stabilizer, and insulators falls as the number of
beams is increased. This encouraging result, however, comes at the price
of increased cooling power, neutron activation, and total magnet volume
and mass. Future work will need to reconcile the cost savings of using
more beams with the increased final focusing cost.

Also, the magnet array half-angles are larger than those used in current
target designs. Additional work is needed to extend target designs to
larger beam angles.

Extrapolating from our 72-beam cases, we predict a magnet lifetime of \~
3 years for a 288-beam case with 10 cm shielding. The magnet array
half-angle, however, would be more than 26°. The lifetime estimate
relies heavily upon largely uncertain radiation damage limits, and thus,
needs to be updated in future work. Data on neutron and γ-ray dose and
fluence limits are needed for superconductors, stabilizers, and
insulators.

Switching from Nb-Ti to one of the new, high-T~c~ superconductors such
as BSCCO-2223 would greatly reduce neutron activation, however, the
radiation lifetimes are even more uncertain. Nb~3~Sn results would be
very similar to those presented for Nb-Ti.

It is worth noting that none of the shielding designs has been optimized
for maximum performance. Given that the fast neutron fluence at the
coils appears to be the limiting factor for magnet lifetime (\~ 2× more
restrictive than the total dose), future work will seek to minimize the
fluence by modifying the shielding design to use materials with larger
fast neutron cross sections. Unfortunately, this also will reduce the
γ-ray shielding effectiveness of the shielding, and thus, the
recirculating power and total dose to the coils likely will increase.
Therefore, updated designs are likely to require an increased shielding
thickness and push the target designs beyond their limits from the
perspective of array half-angle. Future work must explore this trade-off
between final focus shielding and target capabilities and requirements.

Finally, it is also worth noting that subsequent calculations, which
will be presented at the Fourteenth Topical Meeting on the Technology of
Fusion Energy in Park City, Utah in October 2000, have extended the
72-beam magnet lifetime to greater than the expected power plant
lifetime.

**Acknowledgements**

This work was performed under the auspices of the U.S. Department of
Energy by University of California Lawrence Livermore National
Laboratory under contract No. W-7405-Eng-48.

**References**

\[1\] M. E. Sawan, W. F. Vogelsand, and D. K. Sze, University of
Wisconsin Fusion Engineering Program Report UWFDM-438 (1981).

\[2\] R. F. Bourque, W. R. Meier, and M. J. Monsler, Fusion Technol. 21
(1992) 1465.

\[3\] W. R. Meier, R. O. Bangerter, and A. Faltens, Nuc. Inst. and Meth.
A 415 (1998) 249.

\[4\] J. J. Barnard et al., Nucl. Inst. and Meth. A 415 (1998) 218.

\[5\] R. W. Moir et al., Fusion Technol. 25 (1994) 5.

\[6\] W. R. Meier and J. J. Barnard, this proceedings.

\[7\] D. E. Cullen, Law­rence Livermore National Laboratory Report
UCRL-ID-126455, Rev. 2 (1998).

\[8\] J. Sanz, Universidad Nacional de Educacion a Distancia, Lawrence
Livermore National Laboratory Report UCRL-CR-133040 (1999).

\[9\] A.B Pashchenko et al., International Atomic Energy Agency Report
IAEA-NDS-173 (1997).

\[10\] J. F. Latkowski, R. W. Moir, and P. A. House, in press.

\[11\] Y. Isawa, Case studies in superconducting magnets, Plenum Press,
New York (1994).

\[12\] R. A. von Konynenburg et al., Second topical meeting on fusion
reactor materials (1981).

\[13\] P. A. Hahn et al., J. Nucl. Matl. 179 (1991) 1127.

\[14\] M. E. Sawan and P. L. Walstrom, Fusion Technol. 10 (Nov. 1986)
741.

\[15\] D. A. Callahan-Miller and M. Tabak, Nucl. Fusion 39 (Jul. 1999)
883.

![](media/image1.wmf){width="2.579861111111111in"
height="3.560416666666667in"}

Fig. 1. Spot size vs. focus half angle for Cs^+^, 72-beam case.

![](media/image2.png){width="2.7493055555555554in"
height="2.0083333333333333in"}

Fig. 2. View of the neutronics model for the 288-beam case.

![](media/image3.wmf){width="2.8444444444444446in"
height="2.5006944444444446in"}

Fig. 3. Neutron and γ-ray spectra for the 72-beam case

![](media/image4.wmf){width="2.747916666666667in"
height="2.5006944444444446in"}

Fig. 4. Neutron spectra for the 72- and 288-beam cases

Table 1

Key parameters for final focusing magnets

  ----------------------------- ---------- ---------- ---------- ----------
                                                                 

                                                                 

                                Number of                        
                                beams                            

  Parameter                     72         128        200        288

                                                                 

                                                                 

  θ, mrad                       7          5          4          3

  Focus spot radius, mm         1.4        1.0        0.7        0.7

  Beam radius (max), cm         5.0        3.6        2.9        2.1

  Bore radius, cm               6.8        5.0        4.1        3.2

  Winding radius, cm            13.8       12.0       11.1       10.2

  Banding radius, cm            14.4       12.5       11.6       10.7

  Quad outer radius             15.1       13.0       11.9       11.0

  Quad field, T                 3.4        3.1        2.8        2.9

  Field gradient, T/m           24.6       25.6       25.6       28.4

  Array half-angle at target,   11.0       13.2       15.4       17.3
  degrees                                                        

                                                                 
  ----------------------------- ---------- ---------- ---------- ----------

Table 2

Magnet heating and cooling results

  --------------------------- ---------- ---------- ---------- ----------
                                                               

                                                               

                              Number of                        
                              beams                            

  Parameter                   72         128        200        288

                                                               

                                                               

  Prompt heating in coils,    1.19       1.02       0.91       0.76
  mJ/cc                                                        

  Cooling power for final     3.12       3.50       4.02       4.26
  quad, MW~e~                                                  

  Estimated\* total cooling   11-19      13-21      14-24      15-26
  power, MW~e~                                                 

                                                               
  --------------------------- ---------- ---------- ---------- ----------

\* Cooling power is adjusted to correct for scattering and contributions
from the other magnet arrays and auxiliary shielding materials.

Table 3

Magnet dose and lifetime for base cases

  --------------------------- ---------- ---------- ----------- ----------
                                                                

                                                                

                              Number of                         
                              beams                             

  Parameter                   72         128        200         288

                                                                

                                                                

  Annual dose to coils &      39         33         30          25
  insulators (n + γ), MGy/y                                     

  Annual fast neutron fluence 1.7 ×      1.4 ×      1.3 ×       1.0 ×
  to coils & insulators,      10^19^     10^19^     10^19^      10^19^
  n/cm^2^-y                                                     

  Estimated magnet lifetime   0.6-1.3    0.7-1.5    0.8-1.7     1.0-2.0
  based upon annual dose &                                      
  fluence, years                                                

                                                                
  --------------------------- ---------- ---------- ----------- ----------

Table 4

Comparison of the 72-beam cases

  ------------------------------------------- -------------- ------------
                                                             

                                                             

                                              Shielding      
                                              thickness      

  Parameter                                   5 cm           10 cm

                                                             

                                                             

  θ, mrad                                     7              7

  Beam radius (max), cm                       5.0            5.0

  Bore radius, cm                             6.8            6.8

  Winding radius, cm                          13.8           18.8

  Banding radius, cm                          14.4           20.0

  Quad outer radius                           15.1           21.7

  Quad field, T                               3.4            4.6

  Field gradient, T/m                         24.6           24.6

  Array half-angle at target, degrees         11.0           15.6

                                                             
  ------------------------------------------- -------------- ------------