TM-2402-APC

**February 15, 2008**

**Fast-Cycling Superconducting Synchrotrons and Possible Path to the**

**Future of US Experimental High-Energy Particle Physics**

**Henryk Piekarz**

*Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA*

**We outline primary physics motivation, present proposed new
arrangement for Fermilab accelerator complex, and then discuss possible
long-range application of fast-cycling superconducting synchrotrons at
Fermilab.**

1.  **Motivation**

During the past decade developments in the neutrino physics combined
with progress in the cosmological models of dark matter and dark energy
suggest that neutrinos play a very fundamental role in our universe. It
has been determined through solar, atmospheric, reactor and accelerator
experiments that neutrinos change flavor (oscillate) while passing
through matter. This implies that at least two neutrino species have a
non-zero mass \[1\], thus being in a striking contradiction to the
Standard Model (SM), and therefore suggesting existence of the physics
Beyond the Standard Model (BSM). In addition, the possibility of
neutrinos having a small mass may provide a bridge (via e.g. a see-saw
mechanism) to the GUT theories including the origin of mass in the
universe. As a consequence of this new situation a need for the
resolution to the neutrino physics has risen to a level that is not just
complimentary to other high-energy particle physics programs but turns
out to be absolutely necessary to further the understanding of the
microscopic structure and workings of the universe.

In neutrino physics phenomenology neutrinos with physical flavors, ν~α~
(α = e, μ, τ), are assumed to be linear super-positions, through a
unitarity matrix, of neutrino fields with definitive masses ν~i~ (i = 1,
2, 3). A common parameterization for this matrix uses mixing angles,
θ~ij~ = (0, 2π) typically represented by sin^2^θ~ij~, and a CP-violating
phase δ~CP~ = (0, 2π). The current neutrino phenomenology also implies
that two of the neutrino species have relatively close masses while the
mass of the third one is either much heavier (normal hierarchy) or much
lighter (inverted hierarchy) of the "doublet". The lightest (heaviest)
neutrino in the doublet is called ν~1~ (ν~2~) and their squared mass
difference is defined as δm^2^ = m${}_{2}^{2}$ - m${}_{1}^{2}$ \> 0. The
mass difference between m~3~ and m~1,2~ doublet is defined as ∆m^2^ =
\|m${}_{3}^{2}$ - (m${}_{1}^{2}$+ m${}_{2}^{2}$)/2\|. The recent global
analysis \[2\] of solar, atmospheric, reactor and accelerator neutrino
data projects that within a 2σ boundary the δm^2^ = (7.92
${}_{- 0\text{.}\text{09}}^{+ 0\text{.}\text{09}}$) x 10^-5^ eV^2^, and
the ∆m^2^ =(2.4${}_{- 0\text{.}\text{23}}^{+ 0\text{.}\text{23}}$) x
10^-3^ eV^2^ implying that mass of at least one of the neutrino species
is likely to be in the range of (0.01--0.05) eV. We should point out
that in another neutrino data analysis \[3\] this neutrino mass is
(0.04 - 0.10) eV, and some individual experiments, e.g. \[4\], set the
upper mass limit at (0.3) eV, significantly higher than those from the
global fits. The higher mass value is mostly from terrestrial
experiments while the lower one comes from the solar neutrino studies.
In the analysis \[2\] the most likely values of the mixing angle
parameters are also given with sin^2^2θ~13~ =
0.036${}_{- 0\text{.}\text{036}}^{+ 0\text{.}0\text{.}\text{09}}$ (at 2σ
uncertainty level), so it can be even very close to zero.

The neutrino mass can not be directly measured, but as neutrinos pass
through the matter they can change the flavor, the process that is
described as oscillations. The detection of the oscillations would be a
manifestation that neutrinos have mass. The probability of the
oscillation is a function of all the mixing angles and other parameters,
so the potential smallness of the sin^2^2θ~13~ parameter has a strong
impact on the probability of the oscillation, and consequently on the
feasibility of the experiment. In addition, the complexity of the
oscillation function produces typically up to eight-fold degenerate
solutions to the experimental data, adversely affecting oscillation
detection thresholds. As example of how degeneracy of theory parameters
affects sensitivity of the experiment we show in figure 1 the
predictions for the recently proposed NOνA experiment \[5\] at Fermilab.
One can see that combination of the δ~CP~ degeneracy with that of the
∆m^2^ widens the projected neutrino oscillation detection thresholds in
terms of the sin^2^2θ~13~ by more than a factor of 2.

![](media/image1.png){width="3.936111111111111in"
height="3.520138888888889in"}

Fig.1. Sensitivity of NOνA experiment to sin^2^ 2θ~13~ as a function of
δ~CP~,

and for both the negative and the positive sign of ∆m^2^.

It has been shown recently \[6\], however, that there is an experimental
condition when the degeneracy induced by the theory parameters can be
strongly suppressed for the ν~e~ -\> ν~μ~ or ν~μ~ -\> ν~e~ appearance
probability in matter. This appearance probability, P~eμ~, can be
expanded in the small hierarchy parameter α = ∆m${}_{\text{21}}^{2}$/
∆m${}_{\text{31}}^{2}$ and the small parameter sin2θ~13~ as shown below:

P~e,μ~ \~ sin^2^2θ~13~ sin^2^θ~23~ sin^2^\[(1- A)∆\] /(1 -- A)^2^

+/- α sin2θ~13~ ξ sin(δ~CP)~ sin(∆) sin(A∆) F(A,A∆)

\+ α sin2θ~13~ ξ cos(δ~CP~) cos(∆) sin (A∆) F(A,A∆)

\+ α^2^ cos^2^θ~23~ sin^2^2θ~12~ sin^2^(A∆) / A^2^ (1)

where ∆ = ∆m${}_{\text{31}}^{2}$L / 4E, ξ = cosθ~13~ sin2θ~12~ sin2θ~23~
, and A = +/- (2$\sqrt{2}$G~F~ n~e~ E) / ∆m${}_{\text{31}}^{2}$. The L
is the baseline for the neutrino oscillation, and E is the neutrino
energy. The G~F~ is the Fermi coupling constant and the n~e~ is the
electron density in matter. The sign of the second term is determined by
choosing either ν~e~ -\> ν~μ~ (positive), or ν~μ~ -\> ν~e~ (negative)
oscillation channel in the formula (1). One can see that for the sin(A∆)
= 0 all but the first term disappear. This condition is for a nontrivial
solution with $\sqrt{2}$G~F~ n~e~ L = 2π, or in terms of constant matter
density, ρ, equivalent to a magic baseline, L ~magic~:

L ~magic~ \[km\] = 32726 1/ρ \[g/cm^3^\] (2)

With a standard value of ρ = 4.3 g/cm^3^ the magic baseline is \~ 7630
km, but with the PREM (Preliminary Reference Earth Model) density it is
\~ 7250 km long. Naturally, the experiment at magic baseline alone does
not allow for measurement of other parameters. So, data from a second
baseline are needed to fulfill this void. The authors of reference \[6\]
provide analysis strongly suggesting that a combination of data from the
magic baseline with those from the one of \~ 3000 km length would allow
for the determination of the neutrino mass hierarchy (sign of
∆m${}_{\text{13}}^{2}$) and the CP violation (δ~CP~ phase) down to the
values of the sin^2^2θ~13~ parameter by several orders of magnitude
below of those of any current experiment.

Following this observation new proposals are being considered for
sending neutrino beam e.g. from CERN to India \[7\] and from Fermilab to
Europe \[8\], both in 7200-7600 km range. Interestingly, Fermilab
(contrary to CERN) appears also to be the best located for sending a
neutrino beam to a detector at \~ 3000 km away \[8\]. The neutrino
geographical beam paths from Fermilab to Gran Sasso (FNGS, \~7500 km),
and from Fermilab to Mt Whitney, CA (FNMW, \~ 2700 km) is shown in
figures 2a and 2b, respectively. The Gran Sasso is naturally of great
interest because the CNGS detector is already residing there. The Mt
Whitney is also a very interesting location because it is a very tall
(4300 m) mountain of granite rock in a non-seismic area. The other
potential sites at about 2700 km distance from Fermilab are: San
Jacinto, CA and Icicle Creek, WA. Both these sites are considered for a
National Underground Laboratory. All these locations are close to many
West-coast US universities and HEP institutions that would be very
helpful in designing, building and operating a neutrino detector there.

![](media/image2.jpeg){width="2.8965277777777776in"
height="2.1645833333333333in"}
![](media/image3.jpeg){width="2.292361111111111in"
height="2.104861111111111in"}

Fig.2a. Neutrino beam path from Fermilab Fig.2b. Neutrino beam path from
Fermilab

to Gran Sasso, Italy to Mt Whitney, CA

The path of neutrinos through Earth's crust for FNGS and FNMW
experiments is shown in figure3. The maximum depth of the neutrino beam
into the Earth's crust is \~1660 km for the FNGS and \~185 km for the
FNMW. For comparison, the maximum depth of the neutrino path to MINOS
and CNGS experiments (both have baselines of \~ 735 km length) is \~ 10
km. The greater averaged depth of the neutrino path in FNGS and FNMW
experiments has the advantage of a more uniform, and so more
predictable, Earth's matter density which in turn helps in projections
of the neutrino interactions while they are passing through the Earth's
crest.

![](media/image4.jpeg){width="5.971527777777778in"
height="1.7180555555555554in"}

Fig.3. FNGS and FNMW neutrino beam paths through Earth's crest

The neutrino beam considered in ref. \[6\] is that of the proposed
Neutrino Factory \[9\] at CERN. The extreme technological difficulties
for construction of the neutrino factories, however, require very
extensive prior R&D programs, making any practical realization of such a
concept at least (15 - 20) years away. In this situation we proposed in
\[6\] using the high-energy fast-cycling proton synchrotron as the
source of high intensity neutrino beam for these long baseline
experiments. We will show below that with a modest increase of the
detector size relative to those used in the current experiments it will
be possible to reach neutrino oscillation detection thresholds only by a
factor of 6, or so, above the projected ones in \[6\] for the ultimate
Neutrino Factory \[9\].

2.  **Dual Super-Ferric Main Ring as High Intensity Neutrino Source**

*2A. Overview of the DSF-MR accelerator concept*

We assume that the acceptability of any proposed high intensity neutrino
source at Fermilab for long baseline experiments is based on the
following conditions:

-   Allow for a non-interrupted continuity, and upon completion produce
    considerable improvement for the current (MINOS) and planned (NOνA)
    neutrino experiments.

-   Ability to deliver satisfactory neutrino beam intensity for
    experiments with baselines of \~7500 km and \~3000 km.

-   Allow for construction of the new neutrino production beam lines for
    these long baselines fully within the Fermilab proper.

-   Ability to use the existing Fermilab accelerator infrastructure to
    suppress cost, and to speed-up the construction work.

-   Utilize the decades-long experience and potential of Fermilab, BNL,
    LBL and SLAC scientific and technical personnel in synchrotron
    accelerator design, construction and operation.

-   New accelerator complex with neutrino beam lines should be completed
    in a period of time that the followed-up long-term physics program
    will be viewed as much advanced relative to similar contemporary
    programs elsewhere.

We believe that Dual Super-Ferric Main Ring (DFSMR) accelerator as
proposed in \[8\] fulfills well all the above conditions. The outline of
the proposed new Fermilab accelerator complex with DSFMR is shown in
figure 4. When the Tevatron stops its operations it would be replaced
with two rings of fast-cycling synchrotrons (DSFMR).

![](media/image5.jpeg){width="5.985416666666667in"
height="2.8534722222222224in"}

Fig.4. Proposed arrangement of DSFMR at the Fermilab accelerator complex

As the Main Injector is not only the latest addition to the Fermilab
accelerator complex but it is also a well functioning fast-cycling
synchrotron it remains a central part of the proposed new Fermilab
accelerator complex. The main three components of the new accelerator
complex are then: 8 GeV Pre-injector, (8-120) GeV Main Injector, and
(48-480) GeV DSF-MR, all three synchrotrons being the fast-cycling
machines.

The present Pre-injector consists of 0.4 GeV Linac and 8 GeV Booster
that can be used as is for start up. However, both these machines are
the oldest ones, and must be replaced if the proton beam based physics
experiments are to continue at Fermilab into a far future. The most
appealing proposal of a new Pre-injector is the one that consists of a
new 1 GeV Linac with new 8 GeV Booster, both placed in a location that
does not overlap with current Pre-injector. This will allow for the new
machines construction while the physics program continues. As indicated
in figure 3, the new injector is also proposed to become part of the
Project X \[10\]. The Project X would expand the 1 GeV Linac to 8 GeV
with a Booster serving only as the H^-^ stripper ring.

Using two accelerator rings instead of one allows double the repetition
rate for dumping the proton beam onto the neutrino production lines. The
time sequence for beam stacking in Booster, MI and DSFMR accelerators
together with their respected ramping times and beam extraction is shown
in figure 5. The first set of proton pulses from Linac is stacked in the
Booster and accelerated to 8 GeV. This beam batch is then transferred to

![](media/image6.jpeg){width="5.146527777777778in"
height="2.9854166666666666in"}

Fig.5. Time sequence for beam stacking, ramping and extraction onto
neutrino

production targets with DSFMR.

the Main Injector, accelerated immediately to 48 GeV, and then
transferred to one of the DSFMR rings where it will await for a second
proton beam batch from the Main Injector to arrive. The DSFMR ring will
accelerate both batches up to 480 GeV, and then extract them into one or
two neutrino beam production lines, as desired. Some technical details
of the main arc magnet, current leads and power supply designs were
presented in \[11, 12, 13\]. Using the Main Ring tunnel for the DSFMR
allows re-use the existing Tevatron infrastructure (power distribution,
cryogenic support, etc.) for the new accelerator. Very importantly, the
existing Tevatron RF system will also be re-used for the DSFMR after
some necessary expansion and upgrades. In summary, this approach will
save considerable amount of money as well as it will much shorten the
overall DSFMR construction time.

*2B. DSFMR neutrino production lines and the Fermilab proper*

Possible arrangement of the neutrino production lines (shown in figure
6) has been discussed earlier \[8\]. The most important feature for the
neutrino production lines based on the DSFMR accelerator is that these
lines can fit well within the Fermilab proper (figure 7) which extends
\~ 4 km east, and \~ 2.5 km west from the center of the main Ring. We
assumed \~1000 m long meson decay pipes for each of the neutrino
production lines but much longer decay pipes, both in the east and the
west direction, are allowed if needed. The required depth (\~ 240 m for
Mt Whitney path, and \~ 700 m for Gran Sasso path) into which these
decay pipes must go constitutes a great engineering challenge. The fact,
however, that decay pipes are only about 1.5 m in diameter and there is
no need for a human access along the entire pipe length should help the
construction effort and keep the cost at some reasonable level. There
will be shafts to the neutrino production target caves, and to the caves
at the deep ends of each decay pipe where detectors identifying neutrino
production will be located.

![](media/image7.jpeg){width="2.879166666666667in"
height="1.9479166666666667in"}
![](media/image8.jpeg){width="1.9652777777777777in" height="1.8625in"}

Fig.6. Arrangement of neutrino production beam Fig.7. Birds view of the
Fermilab proper.

lines to Mt Whitney and to Gran Sasso. The Main Ring is 2 km in
diameter.

North is up red lines show foot-

prints of neutrino beam lines.

*2C. Projected neutrino beam flux and sensitivity limits with DSFMR*

At present the Main Injector allows for proton bunch intensities, N
*~b~* \~10^11^, without adversely affecting circulating beam phase space
due to e.g. electron cloud effects \[14\]. With the N *~b~* \~ 10^11^
protons per bunch the maximum allowable number of stored protons in the
Main Injector is \~5.4 x 10^13^. As the DSFMR ring circumference is
double in size of the Main Injector and the beam pipe cross-sections are
about the same, one should expect to store \~1.08 x 10^14^ protons in
each of the DSFMR rings. The neutrino beam flux is typically measured by
beam power on production target which is expressed in the formula (3),
where N~p~ is a number of protons on target in units of 10^20^, E~p~ is
the proton energy in units of GeV, and T is the time of exposure in
units of 10^7^ seconds.

Beam Power \[MW\] = ( N~p~ x 1.62 E~p~ ) / ( 1000 x T ) (3)

For proton beam energy of 480 GeV, cycle time of 2 seconds and with 1.08
x 10^14^ protons per cycle the projected DSFMR beam power on target
(POT) is:

POT = (10^-7^ x 1.62 x 480) / (1000 x 2 x 10^-7^) = 8.6 MW (4)

The 8.6 MW exceeds by a factor of 2 the currently acceptable beam power
on a neutrino production target \[15\]. There is a two-fold solution to
this problem: (1) -- reduce beam energy to 240 GeV while keeping the
same cycle time, and (2) -- split and extract 2 beam batches from DSFMR,
each batch onto its own neutrino production target. The first option is
suitable for operations with only one neutrino experiment, while the
second option is suitable for simultaneous operations of two independent
neutrino experiments which is a primary reason for the DSFMR proposal.
Simultaneous extraction onto two production targets with accelerator
cycle time of 2 seconds is equivalent to extracting a beam batch onto
one production target every 1 second. The fact that 4 MW beam power can
be simultaneously available for two neutrino production targets provides
a factor 20 advantage over the current neutrino beam production at
Fermilab (as of November 2006). With the MI beam intensity acceptable at
present (5-6 x 10^13^ per cycle), the HINS would produce maximum beam
power of only 0.8 MW \[8\]. The DSFMR beam power on neutrino production
target also exceeds by factor 2 the proposed future J-PARC and CERN
(SPL) upgrades \[16\].

As the purpose of this note is to provide only a qualitative analysis of
what can be achieved with the DSFMR as a neutrino beam source we use the
neutrino flux for the CNGS experiment with 400 GeV proton beam to
project the neutrino flux with the DSFMR. As shown in \[17\] the
projected neutrino flux at the CNGS detector site (735 km from source)
is \~ 7.5 x 10^-9^ ν~μ~ / pot_m^2^. This makes \~ 4 x 10^-3^ ν~μ~
/p.o.t.\_m^2^ at \~ 1000 m from the production target (excluding
detector acceptance). For the DSFMR this rate increases by the ratio of
480/400 to \~ 4.8 x 10^-3^ ν~μ~ /p.o.t.\_m^2^. Assuming 5 x 10^13^ p/s,
and 2 x 10^7^ seconds/y one obtains \~ 4.8 x 10^18^ ν~μ~ /y at \~ 1000 m
from the production target for each neutrino beam to the far detectors.
The 1000 m distance is a typical decay path for π -\> μ + ν in direct
production of a neutrino beam with proton synchrotrons and it can be
compared to \~700 m path (one leg of a triangle) assumed for a neutrino
production from μ -\> e + ν + $\overline{v}$ decays in the Neutrino
Factory. The π and μ decay paths for the neutrino beam production are
illustrated in figure 8 which shows that with full acceptance of π and μ
the neutrino beam rates per power on target would have to be the same in
both cases. For DSFMR (5 x 10^13^ p/s at 480 GeV) the power on target is
actually 20% higher than for a Neutrino Factory (10^16^p/s at 2 GeV). It
also appears that the μ-decay pipe is typically assumed to be of about
the same cross-section (\~ 1 m^2^) as the π-decay pipe suggesting
expectation of a similar emittance growth of neutrino beams for both
cases.

![](media/image9.jpeg){width="4.363194444444445in"
height="1.0611111111111111in"}

Fig.8. Neutrino production in one step process (π-focusing, DSFMR), and
in

two-step process (π-focusing followed by μ-focusing, Neutrino Factory)

Neutrino Factories \[18, 19\] project typically a useful flux of ν~e~
and ν~μ~ neutrinos \~ 10^20^ /y with the most optimistic expectations of
\~1.8 x 10^20^ ν~μ,e~/y (this latter value was assumed for the
sensitivity limits estimation in \[6\]). So, the DSFMR would have the
ν~μ~ flux about (20-40) times lower than that of the ultimate Neutrino
Factory. It is interesting to observe that with the μ cooling system off
in the neutrino factory \[20\] the projected neutrino beam rate there is
lowered by a factor of 16, but still it would be (1.5-3) times higher
than with DSFMR. This implies that perhaps in the Neutrino Factory the π
meson focusing system is more efficient, or that the overall neutrino
production rate is simply overestimated as there are no actual
measurements yet.

The sensitivity limits scale with the luminosity, L, as 1/$\sqrt{L}$.
The luminosity is a product of a total neutrino flux and detector
acceptance. With the same detector acceptance the limits scale then as
\~ 1/ (Nν~μ~)^1/2^ , which means that the projected limits with the
DSFMR will be higher by no more than a factor of
$\sqrt{\text{40}}$$$`<!-- -->`{=html}6 with respect to those with a
Neutrino Factory. We use the sensitivity projections in reference \[6\]
to scale down the sensitivity reach with DSFMR. The far-away detectors
used in reference \[6\] are of 25 kt fiducial mass. We note that with
some 100 kt fiducial mass for the DSFMR detectors the sensitivity reach
would be only a factor of 3 lower than the one projected in \[6\]. The
expected sensitivity limits with DSFMR, and their comparison to those of
the ultimate Neutrino Factory are shown in figure 9.

![](media/image10.jpeg){width="3.6256944444444446in"
height="2.8756944444444446in"}

Fig.9. Sensitivity reaches as function of sin^2^2θ~13~ for sin^2^ 2θ~13~
(brown), sign of ∆m${}_{\text{31}}^{2}$ (green), and CP violation (blue)
with DSFMR and Neutrino Factory \[6\]. Sensitivity of MINOS and NOνA are
also shown.

The sensitivity limits for sin^2^2θ~13~ projected for the MINOS \[21\]
and NOνA \[5\] experiments are also shown in figure 9. For the DSFMR and
the Neutrino Factories the running times of 4 years with each, neutrino
and antineutrino beams were assumed. The running times with NOνA
experiment is assumed 3 years with each, the neutrino and the
antineutrino beams, and for MINOS 4 years of running is assumed. The
sensitivity projections in figure 9 show that the DSFMR based
experiments exceed by far the sensitivity reach with NOνA experiment and
both MINOS and NOνA experiments are also degenerate by the CP violation
and the sign of ∆m^2^ parameter. The sensitivity limits with DSFMR are
higher though than with Neutrino Factory but the DSFMR can be put into
the operation at least 10 years ahead. The Neutrino Factory has the
advantage over the DSFMR as it also allows study the ν~e~ -\> ν~μ~
oscillations. Consequently, Neutrino Factory may be considered as a
successor to the DSFMR.

*2D. Far-away neutrino detectors with DSFMR*

The detector choice depends on the neutrino energy, which in turn
depends on the energy of the proton beam. In figure 10 we show the mean
neutrino beam energy as a function of the proton beam energy. The higher
the energy of the neutrino the denser the detector can be used. This is
very important because as pointed out in \[22\] it allows for the
neutrinos in the 20 GeV range use the iron based calorimeters, saving
space while increasing the fiducial mass. Most of the current neutrino
experiments apply low-density

![](media/image11.jpeg){width="3.6381944444444443in" height="1.53125in"}

Fig.10. Mean neutrino energy for MINOS (E~p~ = 120 GeV), CNGS (E~p~= 400
GeV)

and projected for DSFMR (E~p~ = 480 GeV)

medium, such as water, scintilator or liquid argon (NOνA). Such approach
requires large detector volumes for a fiducial mass necessary to satisfy
the required detection efficiency. The iron based calorimeters will be
smaller in size, and so much simpler to build, and they tend to have
lower cost and easier operations. In addition, the neutrino detectors
must be placed in the deep caverns, or caves inside the mountain, making
use of cryogens such as liquid argon very difficult. Consequently, if
e.g. the NOνA experiment should proceed it would not only benefit from
the 10 times increased neutrino beam intensity but one perhaps could
also consider using a much less expensive iron-based calorimeter as a
neutrino detector.

The DSFMR can only meet the ultimate limit expectations with a Neutrino
Factory if the fiducial size of the far-away detectors is considerably
increased. This is actually possible with detectors of 1 Mt size as the
proposed ones for the J-PARC-HK and UNO experiments \[23\]. Such
detectors can be constructed as composition of the modular detectors of
a smaller size, e.g. 100 kt over extended period of time while the
physics data are being taken. Using the iron-based calorimeters (instead
of the water Cerenkov detector) certainly facilitates such undertaking.

3.  **Dual Super-Ferric Main Ring as Pre-Injector to VLHC**

The determination of existence (or non-existence) of SM Higgs is the
most important high-energy particle physics goal at present. The LHC is
very well set to discover and investigate Higgs up to mass of 0.8 TeV,
which is nearly an order of magnitude more than the 0.09 TeV mass of SM
highest likelihood. Already the results from the Tevatron suggest that
Higgs mass lower limit is likely to be above 150 GeV, and therefore on
the fringes of acceptability within the Standard Model. In the past
decade developments in the neutrino physics combined with cosmological
theories strongly suggest that neutrinos have mass, a hypothesis that
can not be accommodated within the Standard Model. Consequently, there
is a consensus now that there is a new physics beyond the Standard
Model. Naturally one would like to know the energy scale at which this
new physics occurs. As neutrinos do not carry charge (unlike other
fermions) they can be assumed to have the Majorana mass. Based on this
assumption a model-independent upper bound on the scale, Λ ~Maj~, of
Majorana-neutrino mass generation was outlined in \[24\] as follows:

Λ ~Maj~ = 4πv^2^/$\sqrt{3}$m~ν~ $$ (5)

where v = ($\sqrt{2}$G~F~)^-1/2^ \~ 246 GeV is the SM weak scale, and
m~ν~ is a neutrino mass. By substituting the v = 0.25 TeV with 1, 2 and
5 TeV scales of BSM range we project value of the m~N~ mass as function
of the m~ν~ mass at these higher weak scales. Then by imposing the high
and the low limits on the neutrino mass, m~ν~ , such as e.g. given in
\[2,3,4\], one can project the range of the Majorana neutrino mass,
m~N~, as a function of strength of the weak scale from the BSM model
mass range. The result is shown in figure 11.

![](media/image12.jpeg){width="3.8409722222222222in"
height="2.9618055555555554in"}

Fig.11. Majorana neutrino mass m~N~ for weak scales of 0.25 TeV to 5 TeV
with

bounds on neutrino mass m~ν~ as deduced in Refs. \[2\], \[3\] and \[4\]

For the weak scale of 0.25 TeV the maximum reach of the Majorana
neutrino mass m~N~ is \~ 10^16^ GeV, three orders of magnitude below the
Planck scale. The stronger the weak scale the closer the m~N~ mass gets
to the Planck scale, but interestingly the weak scale does not need to
be higher than \~ 5 TeV to reach the ultimate high m~N~ mass range of
(10^18^--10^19^) GeV. Most theorists believe indeed, that the new
physics will open at $$ 1 TeV mass threshold \[25\]. This is an
interesting observation because it suggests that the mass reach of a
future accelerator may not necessarily need to be much higher than that
of the LHC to begin thorough investigation of the physics from Beyond
the Standard Model. This is, in fact, a primary reason for considering
the DLHC (Double Energy of LHC) as an option for the LHC upgrade in the
future. The LHC energy upgrade, however, will require development of 20
Tesla accelerator magnets which may be very difficult to achieve. In
this situation building the entirely new accelerator with longer
circumference (thus allowing use of LHC type magnets) may be considered
as a reasonable option. One obvious idea is built a scaled-down VLHC
accelerator aiming at mass reach of (5-10) TeV. This would require the
collision energy to be at (50-100) TeV.

At the time the VLHC proposal \[26\] was conceived the adopted guiding
principle was building an accelerator in a tunnel of a largest feasible
circumference to study proton-proton collisions at as high as possible
energy. This approach may have, however, backfired as it has lead to a
project that may have been much too difficult, too expensive, and of too
large a scale to manage. Assuming use of the LHC type magnets in the
final VLHC accelerator stage the collision energy of 56 TeV (4 times the
LHC) is achieved in a circumference of 106 km. A possible placement of
such a new VLHC accelerator in the Chicago area is shown in figure
12.The new VLHC ring is very far away from the areas

> ![](media/image13.jpeg){width="3.861111111111111in"
> height="3.1243055555555554in"}

Fig.12. Possible location of VLHC ring in Chicago area. The rings of

VLHC-2001 and LHC are also shown for comparison.

geologically difficult such as the Troy Bedrock Valley, the Sandwich
Fault, the Michigan Lake, and it does not interfere with the Chicago
city. This makes the construction of the tunnel more feasible from the
civil engineering point of view, and more likely acceptable by the
populace.

The VLHC tunnel will host two accelerator rings, the Low Energy Ring
(LER) and the High Energy Ring (HER). Two 0.5 TeV proton beams from
DSFMR will be simultaneously stacked in the LER ring. Both the LER and
the HER rings use two-bore magnets. After stacking is complete the
energy of both LER beams will ramp to 7.5 TeV, and then beams will
simultaneously transfer to the HER ring. The two beams in the HER ring
will then ramp to the ultimate VLHC energy. At present we assume the HER
ring will use the LHC-type 8 Tesla magnets (VLHC-HER-1). There is,
however, a long-term but realistic possibility of 16 Tesla, and even 20
Tesla accelerator magnets. Such magnets could replace in the future the
8 Tesla magnets allowing for115 TeV (VLHC-HER-2), or 140 TeV
(VLHC-HER-3) of the collision energy, or 10 times that of the LHC.

The VLHC accelerator ring within Fermilab site and the transfer lines
from DSFMR to LER ring are shown in figure 13. For beam transfer from
the LER ring to the HER ring we adopted the concept developed for the
LHC luminosity upgrade with the LER injector accelerator \[27\] sharing
the LHC tunnel. Such arrangement allows for a two-beam single batch
transfer from the low energy ring to the high energy ring inside the
tunnel without by-passing the detectors. Consequently, no transfer lines
in the outside area of the LHC (or VLHC) ring are required.

> ![](media/image14.jpeg){width="4.696527777777778in"
> height="2.59375in"}
>
> Fig.13. VLHC accelerator rings and DSFMR to VLHC transfer lines

The proposed arrangement of the new VLHC does not affect the
long-baseline neutrino physics program, and it allows its continuation
during the construction period as well as after VLHC was built.
Naturally there can be more beam lines originating from the DSFMR for
other fixed target physics programs, or for the detector testing.

A summary of some basic parameters of all synchrotrons involved in the
proposed above new Fermilab accelerator complex is presented in Table 1.
We assume that there will be a new Linac and new Booster built, if the
long range plans for the Fermilab are adopted. For the Booster we
consider both the normal conducting (NC) and the super-conducting (SC)
options. For the latter one the ring circumference would have to be a
bit longer to lower the dipole B-field, so the ramp rate would not
exceed 4 T/s. At 4 T/s the power losses are 4 times higher than with 2
T/s, but they may be considered as practical for a small accelerator
such as the Booster. The new 1 GeV Linac can use either warm or
superconducting cavities. If the warm cavities were chosen their design
could be based on the ones used at present in 0.4 GeV Linac. The
superconducting cavities, on the other hand, require a considerable R&D
effort before considering them for any practical implementation.

Table1. Basic parameters of the synchrotrons in new Fermilab accelerator
complex

+--------------+------------+----------------+-------+---------+-----+
| Synchrotron  | Cir        | Inject         | Max.  | Ramp    | Cy  |
|              | cumference | ion/Extraction |       | rate    | cle |
|              |            |                | B-    |         |     |
|              | \[km\]     | Energy         | Field | \[T/s\] | T   |
|              |            |                |       |         | ime |
|              |            | \[GeV\]        | \[T\] |         |     |
|              |            |                |       |         | \[  |
|              |            |                |       |         | s\] |
+--------------+------------+----------------+-------+---------+-----+
| Booster NC / | 0.474 /    | 1 / 8          | 0.7 / | 7 / 4   | 0.2 |
| SC           | 0.830      |                | 0.4   |         |     |
+--------------+------------+----------------+-------+---------+-----+
| Main         | 3.4        | 8 / 48         | 1.8   | 2       | 1.4 |
| Injector     |            |                |       |         |     |
+--------------+------------+----------------+-------+---------+-----+
| DSFMR        | 6.8        | 48 / 480       | 2.0   | 2       | 2   |
+--------------+------------+----------------+-------+---------+-----+
| VLHC-LER     | 106        | 480 / 7200     | 2.0   | 0.2     | \-  |
+--------------+------------+----------------+-------+---------+-----+
| VLHC-HER-1   | 106        | 7200 / 28800   | 8.0   | 0.005   | \-  |
+--------------+------------+----------------+-------+---------+-----+
| VLHC-HER-2   | 106        | 7200 / 57600   | 16.0  | \-      | \-  |
+--------------+------------+----------------+-------+---------+-----+
| VLHC-HER-3   | 106        | 7200 / 69100   | 20.0  | \-      | \-  |
+--------------+------------+----------------+-------+---------+-----+

4.  **Magnet and Power Supply R&D, Cost Estimate, Timeline**

The fast-cycling superconducting magnets for the DSFMR (and for the
Booster, if desired) are of the most concern. Following the successful
development of the VLHC low-field magnet a design effort was initiated
for a superconducting transmission line that would be suitable for the
fast ramping/fast-cycling magnets. Some preliminary studies of 2 Tesla
magnets operating with a 2 T/s ramp rate \[11\], including the
associated power supply \[12\] and the current leads \[13\] were
recently presented at the MT-20 Conference. It was estimated in \[11\]
that the cryogenic power losses associated with 2 T/s B-field ramping
speed would not exceed some 4 kW for an accelerator of 7 km
circumference (e.g. one ring of the DSFMR). So, for the two rings of
DSFMR the projected cryogenic power loss is of the order of 8 kW, or 1/3
of that of the Tevatron cryoplant of 24 kW. This means that the existing
cryoplant at Fermilab will be sufficient to support also the 8 GeV
Booster if the superconducting magnets were chosen for this machine as
well. The R&D effort for the transmission line conductor including
magnet prototyping is certainly required to produce necessary technical
data for designing the DSFMR magnet. This R&D effort must also comprise
of the power supply and the quench detection/protection systems.
Recently, a strong interest was generated at CERN to develop
superconducting fast-cycling magnets for the PS2 accelerator (a
replacement for the PS). A workshop \[28\] dedicated in part to the
superconducting magnets operating in Hz range is organized at CERN, and
Fermilab was invited to participate in a joint collaborative R&D effort
for the fast cycling superconducting magnets. This development will
certainly help to initiate the R&D for the DSFMR magnet.

In \[8\] a preliminary cost estimate for the construction of the DSFMR
accelerator was given at about \$M300, in the same range (if not much
lower) than the cost of the 8 GeV Linac for the HINS. The cost of two
new neutrino production beam lines was estimated at about \$M200 (most
of the cost is due to the civil engineering work). So, the total cost
was estimated to be in the range of \$M500. By adding some 30%
contingency the overall cost rises to \~ \$M700. With a construction
time spanning over 5-6 years it would mean \$M(120-150) per year on
average. So, even during the tight budget times, such as at present, the
funding agencies may be able to support the DSFMR construction.

5.  **Summary and Conclusions**

At present any new truly large-scale HEP project must wait until physics
data coming from the LHC get sorted out. The LHC is well set to
investigate the Higgs up to 0.8 TeV mass, well beyond the expectations
of the Standard Model. The determination of the Higgs mass is the key to
the prospect for the CLIC/ILC as well as for the Muon Collider. If the
mass Higgs turns out to be only moderately high the LHC will be able to
examine it very thoroughly, and so the basic physics prospect for the
CLIC/ILC or Muon Collider will be to study the spectroscopy of flavor.
Such a study is certainly important to solidify and expand our
understanding of particle interactions, but not yet of a high priority.
On the other hand if the Higgs mass turns out to be very high, or not
even observed at LHC, the required collision energy for the CLIC/ILC as
well as for the Muon Collider will be beyond their technological
feasibilities contemplated at present, and consequently these projects
would be pushed into a very remote future.

It is of utmost importance to continue the experimental high-energy
particle physics program in the US during the LHC era which will be
characterized for some time by uncertainty about options for the future
of HEP. From all the US laboratories it is the Fermilab that has a
unique opportunity to embark on a research program that is both very
important to the high-energy particle physics and also truly
complementary to that of the LHC. The search for the neutrino
oscillations in "7500 km + 3000 km" baselines with DSFMR can be
certainly viewed as such a program. It is likely that the achievable
neutrino theory parameters with DSFMR will in fact turn out satisfactory
for the resolution of the neutrino physics which appears to play a very
fundamental role in understanding the workings of the universe. This
includes not only the microscopic structure of the matter but also the
dark matter and the dark energy of the astrophysics theory. In his
recent remarks to Congress NASA Administrator M. Griffin observed
\[29\]: "*Truly, we study the brush strokes of physics in our particle
accelerators, and (in astrophysics) the grand portrait of those strokes
as it is painted on the night sky".* We believe that the long-baseline
neutrino experiments based on DSFMR accelerator will provide
considerably much more than the "brush strokes" with a reasonable chance
that they will actually paint a masterpiece of physics.

The DSFMR project does not require carry-out R&D effort on a very
fundamental level, or on a large scale. The required magnet R&D and the
prototyping is rather straightforward, inexpensive, and it can be
accomplished in a time span of less than 3 years. One should consider
the use of both the LTS and HTS conductors. The LTS may be more
practical for the smaller machines (Booster or PS2) that must have a
very large bore. Larger bore magnets require a larger core which in turn
may help hide the conductor from the sweeping B-field as suggested in
\[30\], and so the total cryogenic power loss may be acceptable. For the
large machines, such as DSFMR or SFSPS, where the magnetic bore is small
the HTS conductor is preferable \[11\] allowing to substantially reduce
the cryogenic power losses with respect to those with the LTS conductors
suppressing in this way the cost of long term operations. Very
importantly, the DSFMR project will utilize the existing Main Ring
tunnel with Tevatron infrastructure allowing to begin DSFMR construction
at any time. The DFSMR accelerator components and required actions are
listed in Table 2.

Table2. Principal components of DSFMR accelerator

  --------------------------------- -------------------------------------
  **Component**                     **Comment**

  Linac (NC, but SC ok)             Can use existing, preferred new ,1
                                    GeV

  Booster (NC, but SC if new)       Can use existing, preferred new, 8
                                    GeV

  Dual Super-Ferric Main Ring (SC)  New, replaces Tevatron magnets

  RF System                         Use expanded Tevatron RF system

  Injection/Extraction Beam Lines   New transfer lines to be constructed
  --------------------------------- -------------------------------------

Because of necessity to implement as soon as possible a strong
high-energy physics program in the US (after the Tevatron closing) the
new project should demonstrate its ability to be successfully built
within next 6-8 years, and to be of a moderate cost in the same time. We
believe that the DSFMR project can be proven to be just that.

As the DSFMR can extend in a natural way into the VLHC era we present in
Table 3 expectations for maximum energy per parton for the current and
possible future colliders.

Table3. Maximum available energy per parton at various colliders

  --------------- -------------------- ----------------------------------
  Accelerator     CMS energy \[TeV\]   Maximum energy per parton \[TeV\]

  Tevatron        1.8                  0.3

  LHC             14                   2.3

  ILC (CLIC)      1 (3-5)              0.5 (1.5-2.5)

  Muon Collider   1.5                  0.375

  VLHC-HER-1      57.6                 9.6

  VLHC-HER-2      115                  19

  VLHC-HER-3      138                  23
  --------------- -------------------- ----------------------------------

Some arbitrary comparison of the scales of: (1) Physics reach, (2) R&D
effort, (3) Construction effort, (4) Cost, and (5) Time to begin physics
with various possible future HEP projects is shown in Table 4.

Table4. Arbitrary comparison of various possible HEP projects

+------------+--------+--------------+-----------+---------+----------+
| HEP        | P      | R&D Effort / | Civil     | Cost    | Lapsed   |
|            | hysics |              |           |         |          |
| Project    |        | Time \[Y\]   | Con       |         | Time to  |
|            | Reach  |              | struction |         |          |
|            |        |              |           |         | Physics  |
|            |        |              | Effort    |         | \[Y\]    |
+------------+--------+--------------+-----------+---------+----------+
| HINS       | A      | High / 5     | Average   | High    | \> 8     |
|            | verage |              |           |         |          |
+------------+--------+--------------+-----------+---------+----------+
| DSFMR      | High   | Minor / 3    | Average   | Average | \< 8     |
+------------+--------+--------------+-----------+---------+----------+
| Nu-Factory | High   | Very high /  | Very high | Very    | \> 20    |
|            |        | 10           |           | high    |          |
+------------+--------+--------------+-----------+---------+----------+
| CLIC/ILC   | A      | Very high /  | Very high | Very    | \> 20    |
|            | verage | 10           |           | high    |          |
+------------+--------+--------------+-----------+---------+----------+
| Muon       | A      | Very high /  | Very high | Very    | \> 20    |
| Collider   | verage | \> 10        |           | high    |          |
+------------+--------+--------------+-----------+---------+----------+
| VLHC       | High   | Minor / 3    | Very high | Very    | 10       |
|            |        |              |           | high    |          |
+------------+--------+--------------+-----------+---------+----------+

We believe that the DSFMR project is likely to be the best choice for
the US HEP community during the LHC era. It satisfies the necessary high
minded physics goals and it can be put to operation in a rather short
period of time at affordable cost. There are no fundamental
technological issues that must be resolved before embarking on such a
project. This is contrary to the Neutrino Factory, ILC, CLIC and Muon
Collider proposals which seem to be not only technologically very
difficult but likely of the exuberant expectations, with cost and
timeline to be determined only after extensive, long term and costly R&D
programs. The Neutrino Factory parallels, and if its technology permits,
it will exceed the physics reach of DSFMR. The problem is that it has to
succeed in achieving low-emittance muon beam production, and
fast-cycling synchrotron with 10^16^ protons/sec (DSFMR will use
\~10^14^protons/sec).The failure to achieve either of these goals will
put Neutrino Factory on par (or possibly even worse) with DSFMR. In
addition, the civil construction effort for the Neutrino Factory is
extremely difficult as it requires building a 2000 m long muon decay
tunnel (in which beam also re-circulates) of a triangular shape that has
two different and large inclination angles, so the neutrino beams can be
send to both the 3000 km and the 7500 km baselines simultaneously.

One should mention that since the LHC is already built the cost and the
timeline of the VLHC based on the same magnets can be very reasonably
predicted now. This is important because it would bring some stability
to what actually the US HEP can do, and how much support it would be
required to accomplish that goal. In figure 14 possible timelines for
the LHC, DSFMR and possibly the VLHC are shown.

![](media/image15.jpeg){width="5.993055555555555in"
height="1.5472222222222223in"}

Fig.14. DSFMR timeline relative to LHC with possible extension to VLHC

**References**

\[1\] G. Karagiori, et al., "Leptonic CP violation studies at MinBooNE
in the (3+2) sterile

neutrino oscillation hypothesis", *Phys Rev D 75* (013011): 1-8, 2007

\[2\] G.L. Fogli, E. Lisi, A. Marone, and A. Palazzo, "Global analysis
of three-flavor

neutrino masses and mixings", *hep-ph/0506083 v2,* 23 Aug 2005

\[3\] R.N. Mohaptra and A.Y. Smirnov, "Neutrino Mass and New Physics",

*Annu. Rev.Nuc. Sci. 56:569-628 ,* 2006

\[4\] A. Goobar, S. Hannestad, E. Morstell and H. Tu, "A new bound on
the neutrino mass

from the SDSS baryon acoustic peak", *JCAP 06: 019* also
*arXiv:astro-ph/0602155*

\[5\] W. Winter, Nu-Fact 05, "Neutrino Oscillation Physics with a FNAL
Proton Diver",

[*www.Inf.infn.it/conference/nufact05/talks/2WG1/Winter_Proton_Driver_WG1./ppt*](http://www.Inf.infn.it/conference/nufact05/talks/2WG1/Winter_Proton_Driver_WG1./ppt)

June 23, 2005

\[6\] P. Huber, and W. Winter, "Neutrino Factories and the "Magic"
Baseline",

*MPI-PhT/2003-5 and TUM-HEP-499/03,* October 29, 2006

\[7\] S. Agarwalla, S. Choubey, and A. Raychaudhuri, "Neutrino mass
hierarchy and θ~13~

with a magic baseline beta-beam experiment", *CU-PHYSICS-17/2006*

\[8\] H. Piekarz and S. Hays, "Preliminary Consideration of a Dual, 480
GeV, Fast Cycling

Accelerator for Production of Neutrino Beams at Fermilab",
*TM-2381-AD-TD,* 2007

\[9\] P. Huber, M. Lindner, and W. Winter, *Nucl. Phys. B645, 3 (2002),*
also J.S. Berg et al.,

"Cost-effective design for a neutrino factory", *Phys. Rev. Special
Topics --*

*Accelerators and Beams,* **9***, 011001,* 2006

\[10\] D. McGinnis, "A Combined Energy and Intensity Frontier Roadmap",
11/16/07

[www.fnal.gov/directorate/longrange/Steering_Public/Workshop1/07116-9-David-McGinnis.ppt](http://www.fnal.gov/directorate/longrange/Steering_Public/Workshop1/07116-9-David-McGinnis.ppt)

\[11\] H. Piekarz, S. Hays, Y. Huang, G. de Rijk, L. Rossi, "Design
Considerations for

Fast-Cycling Superconducting Accelerator Magnets of 2 Tesla B-Field
Generated by

Transmission Line Conductor of up to 100 kA current", *Int. Conf. on
Magnet*

*Technology MT-20,* Philadelphia, August 27-31, 2007

<http://tdserver1.fnal.gov/project/DSFMR-Future/MT-20-HP-5.pdf>

\[12\] S. Hays, H. Piekarz, H. Pfeffer, B. Claypool, Design
Considerations of a Power

Supply System for Fast Cycling Superconducting Accelerator Magnets of
2Tesla B-

Field Generated by a Transmission Line Conductor of 100 kA Current",
*Int. Conf. on*

*Magnet Technology MT-20,* August 27-31, 2007

<http://tdserver1.fnal.gov/project/DSFMR-Future/MT-20_PS.pdf>

\[13\] Y. Huang, S. Hays, H. Piekarz, G. de Rijk, L. Rossi, "Design
Considerations of a

Pair of Power Leads for Fast-Cycling Superconducting Accelerator Magnets

Operating at 2 Tesla and 100 kA", *Int. Conf. on Magnet Technology
MT-20,* August

27-31, 2007

<http://tdserver1.fnal.gov/project/DSFMR-Future/MT20-CL.doc>

\[14\] M.A. Furman, "A preliminary assessment of the electron cloud
effect for the FNAl

Main Injector", *Fermilab-PUB-05-258-AD,* 23 June, 2006

\[15\] I. Efthymiopoulos, "Mercury Intense target Experiment", *3^rd^
High Power Targetry*

*Workshop,* Bad Zurzach, Switzerland, Sep. 10-14, 2007

\[16\] T. Kobayashi, "Neutrino Super Beams", *Proceedings of Nu-Fact 2,*
July 1-6, 2002,

also W.T. Weng, M.V. Diwan, "Neutrino Beam Facilities and Projects",
*BNL-*

*71228-IR,* April, 2003

\[17\] G. Sirri, "The CNGS neutrino beam", *The 10^th^ Topical Seminar
on Innovative*

*Particle and Radiation Detectors,* Siena, Italy, 1-5 October 2006

\[18\] Neutrino Factory and Muon Collider Studies

<http://www.fnal.gov/projects/muon_collider/> (home page), and also

J.S. Berg et al., "Cost-effective design for a neutrino factory", *Phys.
Rev. Special*

*Topics -- Accelerators and Beams,* **9,** *011001* (2006)

\[19\] A. Blondel, *"Future neutrino beams and muon collider", EPS-ECFA
panel Lisbon*

\(2005\)

\[20\] A. M. Lombardi, *"Neutrino Factories: Machine Issues",*

hepunx.rl.ac.uk/\~edgecock/muons/talks/al-machine-issues.doc

\[21\] D. Petyt, J. Thomas, J. Nelson, "*CC Working Group Summary"*

Webusers.physics.umn.edu/\~petyt/cc/ely05/petyt_cc_summary.ppt

\[22\] A. Donini et al., "A European neutrino program based on the
machine upgrade of the

LHC", *Proceedings of Science, Int. Europhysics Conference on High
Energy*

*Physics, Lisboa, Portugal,* July 21-27, 2005

\[23\]
dpnc.unige.ch/users/blondel/ISS-4/ISS4_NeutrinoDetectorR&D_Soler.ppt

\[24\] J.M. Niczyporuk, "Upper Bound on the Scale of Majorana-Neutrino
Mass

Generation", *International Journal of Modern Physics A,
arXiv:hep-ph/0011045v1*

Nov 2, 2000

\[25\] Ch. Quigg, "The Coming Revolutions in Particle Physics", Talk at
University of

British Columbia" Nov. 15, 2007
(lutece.fnal.gov/Talks/UBCRevolutions.pdf)

\[26\] G. Ambrosio et al, "Design Study for a Staged Very Large Hadron
Collider",

*Fermilab-TM-2149,* June 4, 2001

\[27\] G. Ambrosio et al. "LER-LHC Injector Workshop Summary and Fast
Cycling

Injector in the SPS Tunnel", *Proc. CARE-HHH-APD LHC-LUMI-06*

*Workshop, Valencia,* October 2006, also in:

<http://tdserver1.fnal.gov/project/DSFMR-Future/Lumi-06-paper.doc>

\[28\] L. Rossi, CARE-HHH-APD Workshop on Accelerator Magnet,
Superconductor,

Design and Optimization", CERN, May 19-23, 2008

<http://tdserver1.fanl.gov/project/DSFMR-Future/annoucement-1.pdf>

\[29\] M. Griffin, Remarks to Congress, January 18, 2008

http://tdserver1.fnal.gov/project/DSFMR-Future/Griffin.eml

\[30\] L. Bottura, Superferric PS2, GLM October 8, 2007

<http://tdserver1.fnal.gov/project/DSFMR-Future/Superferric-PS2.ppt>