# Experimental hint for gravitational CP violation

V. Gharibyan

###### Abstract

An equality of particle and antiparticle gravitational interactions holds in
general relativity and is supported by indirect observations. Gravity
dependence on rotation or spin direction is experimentally constrained for
non-relativistic matter. Here a method based on high energy Compton scattering
is developed to measure the gravitational interaction of accelerated charged
particles. Within that formalism the Compton spectra measured at HERA rule out
the speculated anti-gravity possibility for antimatter at a confidence level
close to $100\%$. The same data, however, imply a gravitational CP violation
around 13 GeV energies, by a maximal amount of $(9\pm 2)\cdot 10^{-12}$ for
the charge and $(13\pm 3)\cdot 10^{-12}$ for the space parity. The detected
asymmetry hints for a stronger gravitational coupling to left helicity
electrons relative to right helicity positrons.

##  1 Introduction

Extreme weakness of gravitation makes it the least experimentally investigated
fundamental interaction at sub-atomic scales, with elementary particles. Any
test with a single carrier of the gravitational force, hypothetical graviton,
is unfeasible whereas in the electroweak or strong interactions experimental
results with a photon, W, Z boson or a gluon are readily available at
sufficiently high energies. The weak gravity combined with a rarity and
vulnerability of antiparticles drives any attempt of testing the antimatter
gravitation to its technical limits. Einstein’s general relativity [1], the
currently accepted theory of gravitation, does not distinguish between
particles and antiparticles or their properties such as spin or helicity. The
general relativity is based on universality of gravity and equivalence
principle, and, there is no alternative theory available to predict or
describe violations of these principles in a consistent way. Departures from
perfect spin or particle-antiparticle symmetry are allowed in some quantum
gravitation scenarios [2]. Hence, observations of antiparticle gravitation
could serve as an experimental input for quantum gravity [3]. Additional
motivations for such investigation are the still unexplained matter-dominant
universe [4] and the connection of antimatter’s possible anti-gravity [5] to
the accelerated expansion of the universe [6]. One can also think about a
possible particle-antiparticle gravitational asymmetry and helicity dependence
from an analogy to electroweak interactions, where a photon’s massive
partners, W and Z bosons, are considered responsible for space and charge
parity violations [7]. Thus, possible massive or lower spin gravitons could
introduce similar violations [8] that may remain hidden at low energies and
will become detectable at high energies.

Another possibility to incorporate asymmetric space or charge gravitational
interactions is a modification of vacuum properties described within the
Standard Model Extension (SME) [9] by Lorentz violating terms in Lagrangian.
Such action based approach is further developed for anomalous antimatter
gravity in [10].

Indirect observations of matter-antimatter gravitational asymmetry involve
nuclei with different content of quark-antiquarks in the equivalence principle
Eötvös type experiments [11, 12]. Using $CPT$ conservation the observed
stringent limits for the equivalence principle violating matter could be
expanded to a limit below $10^{-7}$ for the matter-antimatter low energy
gravitational asymmetry [13]. Hughes and Holzscheiter have set limits on the
matter-antimatter gravitational differencies from an equality of particle-
antiparticle cyclotron frequencies [14]. As the source of gravitation,
however, they have used the potential of the local Supercluster while for the
Earth’s potential the derived restrictions are completely lifted. Technical
difficulties for charged antiparticle’s gravitational coupling’s direct
measurements turned physicists’ attention to neutral antimatter tests [15, 16,
17] which may deliver conclusive results soon. The ongoing experiments,
however, are still at low energy, and massive gravitons’ interactions may
remain unseen.

Spin dependent gravitation (for a review see [18]) motivated by Lorentz
violation [19], torsion gravity [20], exchange of pseudoscalar bosons [21] or
few other hypothesis has been constrained by low energy spin-polarized
experiments, such as the test with polarized torsion pendulum [22]. Here also
the high energy could reveal gravitation’s preference for a helicity which is
hidden at low energies.

In this Letter I will demonstrate an extreme sensitivity of a high energy
process - laser Compton scattering - to an antiparticle’s hypothetical anti-
gravity and gravitational charge and space parity violation. Next, applying
the developed formalism to the existing data of the HERA Compton polarimeter,
I will compare the $\gamma$-spectra generated by electrons and positrons to
measure the charge and spin asymmetry for their gravitational interaction.
Systematic effects and prospects for other tests will be discussed at the end.

##  2 Refraction in gravitational field

In an earlier publication, high energy Compton scattering sensitivity has been
shown to a Planck scale dispersive and birefringent vacuum model [23].
Subsequently, I applied the same formalism to the Earth’s gravity assuming the
real gravitational field’s induced refractivity only for the Compton photons
[24]. The refraction, however, also affects the leptons involved in the
scattering [25] in agreement with the equivalence principle. This makes the
ref. [24] conclusions about the general relativity violation invalid [26].

Here I follow the formalism developed by Evans et al. [25] to find a massive
particle’s energy-momentum or refraction relation in a static and isotropic
gravitational field described by the Schwarzschild metric. Combining the
Eq.(3) and Eq.(30) from the reference [25], for a particle at a distance R
from mass M, in a weak gravitational field $GM/R\ll c^{2}$ one can derive a
refraction relation

$c\frac{P}{\cal E}=\frac{v}{c}+\frac{2GM}{c^{2}R},$ (2.1)

where $G$ is the gravitational constant, $c$ is the speed of light and ${\cal
E},P,v$ are energy, momentum, velocity of the particle. This relation is also
valid for massless particles: at $v=c$ it describes the photon refraction in a
gravitational field in a form derived by many authors; see ref. [27] and
references therein, or, for a more recent reference, see ref. [28]. The second
term in Eq.(2.1) is a scaled gravitational potential $U(G,M,R)=-GM/R$ of the
gravitating mass. This term can be dropped from Eq.(2.1) unless there is a
change in the potential

$\Delta U=U\frac{\Delta G}{G}+U\frac{\Delta M}{M}-U\frac{\Delta R}{R}.$ (2.2)

Indeed, at $\Delta U=0$ the physical processes (involving one or more
particles) are not altered by the extra gravitational term in Eq.(2.1) since
the potential $U$ cancels in energy-momentum conservation. Situation changes
with $\Delta U\neq 0$. Thus, for $\Delta R\neq 0$ case, differentiated
Eq.(2.1) describes particle’s gravitational energy change (frequency red/blue
shift for $v=c$) or deflection - using the principle of least action. While
these are classical gravity processes validated by multiple measurements, the
first term in Eq.(2.2), $\Delta U_{G}=U\Delta G/G$, violates equivalence
principle and has intensively been constrained by pendulum null experiments
with different materials - all for the non-relativistic ($c=\infty$) case (see
ref.[11] and references therin). Thus, Eq.(2.1) follows from general
relativity in a weak field (metric is replaced by gravitational potential) and
describes relativistic gravitational effects in accord with the equivalence
principle.

To allow departure from the equivalence principle let us retain the
interaction strength $G$ for matter particles and use a different strength
$G_{p}$ for antimatter leptons to write Eq.(2.1) for positrons in the
following form

$c\frac{P}{\cal E}=\frac{v}{c}-2\frac{U}{c^{2}}\biggl{(}1+\frac{\Delta
G_{p}}{G}\biggr{)},$ (2.3)

with $\Delta G_{p}=G_{p}-G$. For an anti-gravitating positron $G_{p}=-G$.

In a similar manner, within the spin affected gravitation, we can assign an
interaction constant $G_{-}$ to particles possessing a negative(left) helicity
and modify the Eq.(2.1) to include a helicity dependent term $\Delta
G_{-}=G_{-}-G$

$c\frac{P}{\cal E}=\frac{v}{c}-2\frac{U}{c^{2}}\biggl{(}1+\frac{\Delta
G_{-}}{G}\biggr{)}.$ (2.4)

Positive(right) helicity particles’ coupling constant $G_{+}$ is assumed to
provide an average $(G_{-}+G_{+})/2=G$ for unpolarized or zero helicity case,
so that $\Delta G_{-}=-\Delta G_{+}$.

Anomalous dispersion or refraction relations similar to the Eq.(2.3) or
Eq.(2.4) are often applied for vacuum, within the context of action based
Lorentz violation [29, 30]. Such models have an advantage to access modified
dynamic properties (cross-sections) of considered processes though stringent
observational and experimental limits, in particular from a Compton scattering
test [33], exist for Lorentz violating vacuum [31].

Here we limit ourselves exceptionally with kinematics in a real gravitational
field to investigate how the hypothetical refractions by Eq.(2.3) and Eq.(2.4)
are affecting the high energy laser Compton process.

Similar to Eq.(2.3) assumption has recently been considered in hypothetical
vacuum Cherenkov radiation formalism to constrain charge parity violation in
gravitational field [32].

##  3 The Compton process affected by gravity

Using energy-momentum conservation with Eq.(2.1) and Eq.(2.3), when in the
Earth’s gravitational field a photon scatters off a positron with energy
${\cal E}$, the Compton scattering kinematics is given by (from here on
natural units are assumed)

${\cal
E}x-\omega(1+x+\gamma^{2}\theta^{2})+4\omega\biggl{(}1-\frac{\omega}{{\cal
E}}\biggr{)}\gamma^{2}U\frac{\Delta G_{p}}{G}=0,$ (3.1)

where $x=4\gamma\omega_{0}\sin^{2}{(\theta_{0}/2)}/m$, with $m$ and
$\gamma={\cal E}/m$ being the mass and Lorentz factor of the initial positron,
respectively. The initial photon’s energy and angle are denoted by
$\omega_{0}$ and $\theta_{0}$, while the refraction of Eq.(2.1) is in effect
for the scattered photon with energy $\omega$ and angle $\theta$; the angles
are defined relative to the initial positron. This kinematic expression is
derived for weak gravity and high energies, i.e., the $\mathcal{O}(U^{2})$,
$\mathcal{O}(\theta^{3})$, and $\mathcal{O}(\gamma^{-3})$ terms are neglected.
In this approximation the refraction effect of Eq.(2.1) for the initial laser
photon is negligible. For the initial and scattered positrons the refraction
of Eq.(2.3) is applied. To determine the outgoing photon’s maximal energy,
Eq.(3.1) is solved for $\omega$ at $\theta=0$ with the following result:

$\omega_{max}={\cal E}~{}\frac{b+q-\sqrt{b^{2}+q(q-2b+4)}}{2\,q},$ (3.2)

where $b=1+x$ and $q=-2\gamma^{2}U\Delta G_{p}/G$. Thus, in high energy
Compton scattering the small factor $U\Delta G_{p}/G$ is amplified by
$\gamma^{2}$, allowing one to measure it by detecting the extreme energy of
the scattered photons $\omega_{max}$, or positrons ${\cal E}-\omega_{max}$
(Compton edge).

In order to estimate the method’s sensitivity, I calculate the Compton edge
from the Eq.(3.2) for an incident photon energy 2.32 eV (the widely popular
green laser) in the Earth’s gravitational field
($U=-GM_{\oplus}/R_{\oplus}=-6.95\times 10^{-10}$), at different energies of
the accelerator leptons. The resulting dependencies for a matter (electron)
gravity and antimatter (positron) anti-gravity are presented in Fig. 1.

Figure 1:  The maximal energy of Compton scattered photons (Compton edge) and
its dependence on the initial lepton energy for a head-on collision with 532nm
laser light, in the Earth’s gravitational field. The solid line is for matter
gravity ($e^{-}$, electron, $G$) while the dashed line shows antimatter anti-
gravity case ($e^{+}$, positron, $-G$). The dotted line corresponds to
gravitationally sterile right (positive helicity) Compton photons
($\mathbf{\gamma}$, $G_{+}=0$). Names of $e^{+}e^{-}$ accelerators are printed
at the upper part.

The plot shows considerable sensitivity, which grows toward high energies in a
range available to accelerating laboratories. For handling measurement’s
systematic errors, from an experimental point of view, it is more precise to
measure a relative asymmetry rather than absolute Compton edge energy.
Therefore, we form an asymmetry of Compton edges measured on positrons
($\omega_{max}^{p}$) and electrons ($\omega_{max}^{e}$)

$A=\frac{\omega_{max}^{p}-\omega_{max}^{e}}{\omega_{max}^{p}+\omega_{max}^{e}}$
(3.3)

and use Eq.(3.1) to find the charge parity gravitational violation magnitude

$\Delta U_{Gp}\equiv U\frac{\Delta
G_{p}}{G}=-\frac{1}{2\gamma^{2}}\cdot\frac{A(1-A)(1+x)^{2}}{(1+A)(2Ax+A-1)}.$
(3.4)

For evaluating a sensitivity of the laser Compton process to the spin
dependent gravitation let’s investigate left helicity photon scattering off
unpolarized (zero mean helicity) leptons’ beam. According to helicity
conservation, the scattered gamma-quantum will retain the helicity of the
initial photon at Compton edge energies [34]. Hence we apply the helicity
modified refraction relation of Eq.(2.4) to the initial and final photons,
reserving the refraction of Eq.(2.1) for the initial lepton. After scattering
the leptons become longitudinally polarized acquiring
$P_{l}=x(2+x)/(1+(1+x)^{2})$ portion of the initial photon circular
polarization [35, 36]. Therefor, for the scattered lepton, the term $\Delta
G_{-}/G$ in energy-momentum relation (2.4) must be scaled by a factor
$-P_{l}/2$, where the $-1/2$ coefficient counts for half spin and positive
helicity of the lepton. This modifications will bring the Eq.(3.2), Eq.(3.4)
for the charge parity case to

$\omega_{max}^{-}={\cal
E}~{}\frac{\sqrt{b^{2}+4u(u+x+P_{l}-1)}-b+2u(1+P_{l})}{2u(2+P_{l})},$ (3.5)

and, with a measured energy asymmetry
$A_{-}=(\omega_{max}^{-}-\omega_{max}^{0})/(\omega_{max}^{-}+\omega_{max}^{0})$,
to

$\Delta
U_{G-}=\frac{1}{2\gamma^{2}}\cdot\frac{2A_{-}(1-A_{-})(x^{2}+2x+2)(1+x)^{2}}{A_{-}^{2}x_{1}+A_{-}x_{2}-(2x^{2}+3x+2)},$
(3.6)

for the space parity case. In the above equations the upper index ($-,0$)
stands for the scattered photon’s average helicity and the following
assignments are made: $u=-2\gamma^{2}U\Delta G_{-}/G$, $\Delta U_{G-}=U\Delta
G_{-}/G$, $x_{1}=8x^{3}+22x^{2}+21x+6$, $x_{2}=4(x^{3}+x^{2}-0.5x-1)$. Energy
dependence of Eq.(3.5), if the Earth’s gravity attracts only left helicity
particles, is plotted on the Fig. 1. From the plot and formulas we can
conclude that Compton process sensitivity to the gravitational space parity
violation is sufficient for introducing a Compton edge sizable shift in a
scenario of the helicity dependent gravitational field.

For estimating the sensitivity in Fig. 1 the Earth’s gravitational potential
$6.95\cdot 10^{-10}$ is used. There is though a much more greater
gravitational field at the Earth’s surface, the largest, local Supercluster’s
potential [14] with a magnitude $3\cdot 10^{-5}$. For gravitational effects
induced by the third term proportional to $\Delta R/R$ in Eq.(2.2), the
Earth’s potential prevails (due to large $1/R$ factor) while in our case, for
the first term in Eq.(2.2) with $\Delta G/G$, the local Supercluster potential
contribution is dominant. Exact potential selection, however, is important
only when separating the $\Delta G/G$ contribution from the $\Delta U$ factor.
The Compton scattering could measure only the factors $\Delta U_{Gp}$ or
$\Delta U_{G-}$.

Besides the gravitation, other interactions also may alter energy-momentum
relation [37, 38]. For the Compton process a background electromagnetic field
is the main competitor to gravity, and, since electric fields are usually
shielded by conductive beam pipes, let’s estimate influence of magnetic
fields. According to Eq.(1.1) from the reference [37], the maximal impact to
energy-momentum relation for photons in a magnetic field $B$ is presented by

$\frac{P}{\cal E}=1-\frac{14}{45}\frac{\alpha^{2}}{m^{4}}B^{2},$ (3.7)

where $\alpha$ is the fine-structure constant. Hence, refractivity created by
a 4 T superconducting magnet is about $8\cdot 10^{-21}$ and that of Earth’s
magnetic field is $10^{-25}$. These tiny effects are still experimentally
unreachable, and, compared to the gravitational potential magnitude (either
the Supercluster’s $\sim 10^{-5}$ or the Earth’s $\sim 10^{-9}$) in the
Eq.(2.1), are completely negligible.

##  4 Experimental results

The high-energy accelerators where laser Compton facilities have been operated
for years, are listed on the upper energy scale of Fig. 1. As can be seen from
the plot, 6 GeV storage rings have low sensitivity while the higher energy
colliders (HERA, SLC, LEP) have a great potential for detecting gravity
related energy shifts. This is true for the HERA and SLC Compton polarimeters
but not for the LEP polarimeter, which has generated and registered many
photons per machine pulse [39]. In this multi-photon regime, any shift of the
Compton edge is convoluted with the laser-electron luminosity and can-not be
disentangled and measured separately. Unlike the LEP, the SLC polarimeter
operated in multi-electron mode and analyzed the energies of interacted
leptons using a magnetic spectrometer [40]. However, at SLC only the electron
beam was polarized, and positron data are missing. Hence, we turn to HERA,
which has recorded Compton measurements for both the electrons and the
positrons. At the HERA transverse polarimeter Compton photons are registered
by a calorimeter in single particle counting mode. A recorded Compton spectrum
produced by $514.5$nm laser scattering on $26.5~{}GeV$ electrons, from
ref.[41], is shown in Fig. 2

Figure 2:  HERA polarimeter Compton $\gamma$-spectrum produced by laser
scattering on $26.5~{}GeV$ electrons, on top of background Bremsstrahlung with
fit results. The inset displays the background subtracted Compton spectrum.
Vertical lines show measured values of the Compton ($\omega_{max}$) and
Bremsstrahlung (${\cal E}_{e-}$) maximal energies.

superimposed on a background Bremsstrahlung distribution. In contrast to
Compton scattering, in the Bremsstrahlung process the momentum transfer is not
fixed, and any small refractive effect is smeared out and becomes negligible
[42]. Hence, following the analysis in ref. [42], I calibrate the energy scale
according to the maximal Bremsstrahlung energy which is found by fitting a
convolution of parent energy distribution ${d\Sigma}/{d\omega}$ with the
detector response gaussian function,

$F(E_{\gamma})=N\int^{E_{m}}_{0}\frac{d\Sigma}{d\omega}\frac{1}{\sqrt{\omega}}\exp\Biggl{(}{\frac{-(\omega-
E_{\gamma})^{2}}{2\sigma_{0}^{2}\omega}\Biggr{)}d\omega},$ (4.1)

to the Bremsstrahlung spectrum. $\sigma_{0}$ and $E_{\gamma}$ in the fitting
function denote the calorimeter resolution and detected photon’s energy
respectively while the normalizing factor $N$ and maximal energy $E_{m}$ are
free fitting parameters. The fit is performed using MINUIT [43] and the
integral (4.1) is calculated numerically applying the Gaussian quadrature
algorithm. The same fitting function with the Bremsstrahlung parent
distribution replaced by the Compton scattering differential cross-section
${d\Sigma_{C}}/{d\omega}$ is applied to the background subtracted spectrum to
find the Compton edge at $\omega_{max}^{e0}=12.70\pm 0.02$ GeV. Here the upper
indexes denote (scattered) lepton type, helicity and the 0 stands for a
spectrum summed over the laser left and right helicities. The fit results
together with fit quality estimates are shown in Fig. 2. The absolute value of
the Compton edge is calculated from 3 measurements – Bremsstrahlung and
Compton edges $B_{max}$ and $C_{max}$ in ADC units, and electron beam energy
$E_{beam}$ in GeV – by a formula  $\omega_{max}=E_{beam}C_{max}/B_{max}$. More
details about the analysis and experimental setup can be found in the ref.
[42].

The same analysis procedure is applied to a HERA polarimeter Compton spectrum
that was generated with left helicity photons scattered on $27.5~{}GeV$
positrons and has been reproduced in Fig. 8 of ref. [44]. As it mentioned
above, left helicity laser photons are generating the same (negative) helicity
scattered positrons at the Compton edge ($\omega_{max}^{p-}$). The resulting
plots with fit quality outcomes are displayed in Fig. 3.

Figure 3:  A similar plot to Fig. 2 for positrons with energy $27.5~{}GeV$.
The Compton edge energy for anti-gravitating positrons is indicated by a
vertical line $\omega_{max}(-G)$.

Comparing the obtained Compton edge $\omega_{max}^{p-}=13.80\pm 0.02$ GeV with
the photons’ maximal energy for the anti-gravitating positrons $25.9$ GeV,
derived from Eq.(3.2), one can conclude without any advanced systematic error
analysis that anti-gravity for the positrons is ruled out. We can estimate
accuracy of this statement by assuming an absolute energy calibration scale of
$0.14~{}GeV$ as it calculated in ref. [42]. Thus, antimatter’s anti-gravity is
excluded within more than $85\sigma$ confidence interval.

Using only the quoted statistical errors for the $\omega_{max}^{e0}$,
$\omega_{max}^{p-}$ we obtain a positron-electron and negatve-zero helicity
Compton edge asymmetry
$A_{ep0-}=0.01297\pm 0.0013.$ In order to account for the different energies
of accelerated electrons and positrons $26.5$ and $27.5$ GeV, the measured
maximal energies in the asymmetry calculation have been normalized to $13.10$
and $13.87$ GeV for the electrons and positrons, respectively. These are the
expected Compton edge values from Eq.(3.2) or Eq.(3.5) in the absence of
gravitational anomaly, at $\Delta G_{p}=0$ or $\Delta G_{-}=0$ respectively.

Since the spectra for electrons and positrons are detected with the same
experimental setup, i.e. with the same laser, geometry and detector, both
measurements will experience the same systematic influences that will cancel
out or reduce greatly in the asymmetry of Eq.(3.3). Hence, we omit systematic
corrections with associated errors applied to polarization or energy
measurements (as described in the refs. [41, 42, 44, 45]), in order to analyze
instrumental errors specific to the detected asymmetry which we rewrite in a
more convenient form:

$A_{ep0-}=\frac{\eta_{p}x_{e}(1+x_{p})-\eta_{e}x_{p}(1+x_{e})}{\eta_{p}x_{e}(1+x_{p})+\eta_{e}x_{p}(1+x_{e})},$
(4.2)

where $\eta=C_{max}/B_{max}$ is a ratio of the measured Compton and
Bremsstrahlung edges, $x$ is the kinematic factor with indexes $e$ and $p$
denoting the measurement with electrons and positrons respectively.

Uncertainty of the factor $x_{e,p}=4{\cal
E}_{e,p}\omega_{0}\sin^{2}{(\theta_{0}/2)}/m^{2}$ is dominated by the lepton
beam energy spread while contribution of the other constituents is negligible:
$\sigma(\omega_{0})/\omega_{0}\approx 10^{-5}$, $\sigma(m)/m\approx 3\cdot
10^{-7}$, $\Delta(\theta_{0})\\!\approx\\!2~{}mrad\Rightarrow$
$\Delta\sin^{2}{(\theta_{0}/2)}\approx 3\cdot 10^{-6}$. Therefore, HERA
leptons’ energy spread $\sigma({\cal E})/{\cal E}\approx 10^{-3}$ will
introduce a systematic uncertainty $7.9\cdot 10^{-4}$ to the measured
asymmetry. Since the electron and positron measurements are considerably
separated in time, one of important potential sources for a false asymmetry
could be detector aging and degraded performance. This assumption could be
checked by measuring the calorimeter resolution from the spectra edges’ slops
- the same energy resolution $\sigma_{0}=0.24$ for both spectra indicates the
same, non-degraded, response of the calorimeter.

A major energy correction factor, detector non-linearity, applied to each
measured Compton edge will largely cancel in the asymmetry. However, assuming
a possible change of detector’s linearity we apply a non-linearity correction
(as described in ref. [42]) which will scale the ratio $\eta\to\eta(1+f{\cal
E}(1-\eta))$ with a factor $f=0.001GeV^{-1}$. Limiting the possible change of
non-linearity factor to 10%, from error propagation in the Eq.(4.2), we derive
an associated conservative systematic uncertainty of $9.6\cdot 10^{-4}$ for
the asymmetry which is affected negligibly by the correction.

A correlated error could potentially be induced by the detector spatial non-
uniformity which affects the Compton edge absolute energy determination in
case of Compton and Bremsstrahlung beams vertical separation [42]. In the
asymmetry, however, the non-uniformity is negligible when the Bremsstrahlung
from electrons and positrons overlap (Eq.(4.2) effectively depends on

$\eta_{p}/\eta_{e}=(C_{max}^{p}/C_{max}^{e})\cdot(B_{max}^{e}/B_{max}^{p})$

ratio). This is the usual case with the calorimeter centered on the Compton
beam during polarization measurements. Then, the electron and positron
Bremsstrahlung vertical overlap is provided by geometrical constraints, flat
orbit requirements and the polarimeter setup location at HERA West –- away
from the routine beam-tuning regions at the lepton-proton interaction points
in HERA East, North and South. In order to depart from the assumed $100\%$
spatial correlation of $e^{-}$ and $e^{+}$ Bremsstrahlung beams, we allow a
$10\%$ mismatch (correlation coefficient $C_{f}=0.9$) to estimate the detector
non-uniformity influence on the measured asymmetry. Thus, the quoted $1\%$
spatial non-uniformity [41] will result in a $2.2\cdot 10^{-3}$ correlated
systematic error in the asymmetry according to correlated error propagation
formula

$(\delta A)^{2}=(dA_{p})^{2}+(dA_{e})^{2}-2C_{f}dA_{p}dA_{e},$ (4.3)

with $dA_{p}=\frac{\partial A}{\partial\eta_{p}}\Delta\eta_{p}$,
$dA_{e}=\frac{\partial A}{\partial\eta_{e}}\Delta\eta_{e}$ and
$\Delta\eta_{p}/\eta_{p}=\Delta\eta_{e}/\eta_{e}=0.01$.

Other minor instrumental false asymmetry sources are electronic pedestal
offsets, estimated to be $\pm 4MeV$ with $\approx 3\cdot 10^{-4}$ contribution
to asymmetry and luminosity dependent pile-up photons. The latter amounts to
0.02 and 0.0015 photons/bunch for the electrons and positrons respectively,
and, in our case, will tend to reduce any true asymmetry so, it can’t be
responsible for the observed effect. An ignorable, about the order of m,
contribution to electron-positron asymmetry is coming from Bremsstrahlung edge
charge dependence. The quoted and calculated errors are listed in the Table 1.

Table 1: Errors of the measured asymmetry $A=1.3\cdot 10^{-2}$.

Source | Magnitude (rel.) | Error $\Delta A$
---|---|---
Statistical fluctuations | $1.4\cdot 10^{-3}$ | $1.3\cdot 10^{-3}$
Laser frequency shift | $10^{-5}$ | $\approx 0$
Electron mass’ error | $3\cdot 10^{-7}$ | $\approx 0$
Interaction angle drift | $3\cdot 10^{-6}$ | $\approx 0$
HERA-e energy spread | $10^{-3}$ | $7.9\cdot 10^{-4}$
Non-linearity change | $10^{-1}$ | $9.6\cdot 10^{-4}$
Beams vertical mismatch | $10^{-1}$ | $2.2\cdot 10^{-3}$
Electronic pedestal shift | $2.9\cdot 10^{-4}$ | $3\cdot 10^{-4}$
Pile-up photons | $7.5\cdot 10^{-2}$ | $\leq 0$
$e^{+}$ bremsstrahlung edge | $7.2\cdot 10^{-5}$ | $\approx 0$

There are also potential contributions from chiral sources collected in the
Table 2. To estimate the magnitudes of these effects I have explored the HERA
transverse polarimeter setup simulation code [45].

Table 2: Systematic contributions from chiral sources.

Source | Magnitude | Error $\Delta A$
---|---|---
Magnetic field | $50~{}\mu T$ | $2.3\cdot 10^{-26}$
Earth’s spin | $2\cdot 10^{-23}~{}eV$ | $8.0\cdot 10^{-30}$
Lepton polarization | 0.6 | $3.1\cdot 10^{-6}$
Laser linear polarization | 0.2 | $5.4\cdot 10^{-7}$

A tiny effect from the stray magnetic fields have been calculated using
Eq.(3.7). The Earth’s rotation gravitomagnetic impact on elementary particles
amounts to $\hbar g/c=2.2\cdot 10^{-23}$eV, where $g$ is the gravitational
acceleration in the laboratory [46]. This contribution to the measured
asymmetry is also negligibly small. Compared to the birefringent magnetic
field and Earth’s spin, the instrumental chiral effects, responsible for false
asymmetries, are larger by many orders of magnitude. The effects are induced
by a change of laser polarization either linear or circular, the latter in
convolution with the lepton spin. An energy dependence of the induced
asymmetries (for 100% polarized leptons) is plotted in Fig.4 for HERA
polarimeter parameters. Though the mentioned polarized effects can not
directly affect the Compton edge photons to alter the observed asymmetry, an
energy smearing and spatial non-uniformity of the detector can mimic a Compton
edge shift. Simulations with conservatively high values of the lepton and
linear light polarizations show artificial asymmetries below $10^{-5}$ value.

Figure 4:  Asymmetries in Compton scattering associated with the initial
photon’s polarization (linear $\lambda_{l}$ and circular $\lambda$) changes.
Analyzing powers (asymmetries for the cases
$\lvert\Delta\lambda_{l}\rvert=1,\lvert P_{e}\Delta\lambda\rvert=1$) of the
HERA transverse polarimeter setup.

With a quadratic sum of the estimated systematic and statistical errors the
measured asymmetry and its error become

$A_{ep0-}=(1.293\pm 0.286)\cdot 10^{-2},$ (4.4)

which differs from zero by more than $4\sigma$ confidence. Within an extreme
conservative approach, a linear summation of all the errors reduces the
deviation to $3.6\sigma$ confidence interval.

Separate contributions of the gravitational charge and space parity violations
can’t be derived from this asymmetry alone. Instead one can assume space P
parity conservation and calculate maximally possible electron-positron charge
C parity violation by inserting the observed asymmetry into Eq.(3.4):

$\Delta U_{Gp}=(-9.0\pm 2.0)\cdot 10^{-12}.$ (4.5)

In a similar way, within a perfect C parity conservation one will have maximal
P parity violation magnitude using Eq.(3.6):

$\Delta U_{G-}=(1.28\pm 0.29)\cdot 10^{-11}.$ (4.6)

In a general case of C&P violation the C and P symmetries are violated to
lesser degrees. Obtained signs of violations correspond to a stronger
gravitational coupling for the left helicity electrons relative to the right
helicity positrons.

##  5 Conclusions

Applying a gravitational field-induced refraction and assuming an equivalence
principle violation in a general form $\Delta G_{p}/G$ for positrons and
$\Delta G_{-}/G$ for helicty, an outstanding sensitivity has been demonstrated
for the high energy Compton scattering to such gravitational anomaly. Within
the developed formalism, the HERA Compton polarimeter’s recorded spectra with
electrons and positrons strongly disfavor the positron’s anti-gravity and show
a significant deviation of the $\Delta G_{p}/G$ or $\Delta G_{-}/G$ from zero.
The last claim is based on a detected $0.013$ energy asymmetry, which is a
large number compared to the laser and lepton beam energy relative uncertainty
of $10^{-5}$ and $10^{-3}$, respectively. The remaining source of a possible
systematic energy error is the detector that is greatly eliminated from final
result by using the asymmetry instead of absolute energy measurements.
However, additional uncorrelated systematic errors may impair the outcome and,
claiming a definite observation of CP parity violation at high energy
gravitational interactions would require the following:

– a thorough analysis of many Compton spectra accumulated and recorded by the
HERA during its running period;

– elimination of possible electroweak sources that can mimic such result;

– experimental verification at other accelerators.

In the absence of these, the measured electron-positron asymmetry can only be
considered as a hint for the gravitational symmetry breaking and an invitation
for further studies. New experiments, however, will require future
$e^{-}e^{+}$ machines with sufficiently high $\gamma$ or a precise setup on
the currently running 6 GeV accelerator PETRA-III with the highest positron
energy available. Anyway, it is worth the efforts since high energy violation
of the equivalence principle and gravitational CP parity could reveal an
interaction to massive or lower spin gravitons.

## Acknowledgement

I thank B. Sobloher and S. Schmitt for providing details about the positron
generated spectra, and R. Brinkmann for details about the electron measurement
and the HERA. I’m thankful also to A. Buniatyan and K. Balewski for useful
discussions.

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# A Reference Architecture for the American Multi-Modal Energy System

Dakota J. Thompson, Amro M. Farid,

###### Abstract

The American Multimodal Energy System (AMES)is a systems-of-systems comprised
of four separate but interdependent infrastructure systems: the electric grid,
the natural gas system, the oil system, and the coal system. Their
interdependence creates the need to better understand the underlying
architecture in order to pursue a more sustainable, resilient and accessible
energy system. Collectively, these requirements necessitate a sustainable
energy transition that constitute a change in the AMES’ instantiated
architecture; although it leaves its reference architecture largely unchanged.
Consequently, from a model-based systems engineering perspective, identifying
the underlying reference architecture becomes a high priority. This paper
defines a reference architecture for the AMES and its four component energy
infrastructures in a single SysML model. The architecture includes (allocated)
block definition and activity diagrams for each infrastructure. The reference
architecture was developed from the S&P Global Platts (GIS) map data pro data
set and the EIA Annual Energy Outlook dataset.

###### Index Terms:

American multi-modal energy system, Model-Based Systems Engineering, Reference
Architecture, SysML, Energy Systems

##  I Introduction

The American Multimodal Energy System (AMES) is a _system-of-systems_
comprised of four separate but interdependent infrastructure systems. The
electric grid, natural gas system, oil system, and coal system comprise the
essential infrastructure that meet the energy demands of the 21st century in
America. While each of these individual systems constitute a value chain in
their own right, they also enable and support the value chains in the other
energy systems. This interdependence creates the need to better understand the
underlying architecture in order to pursue a more sustainable, resilient and
accessible energy system. Each of these three general requirements are
discussed in turn.

From a sustainability perspective, the decarbonization of the AMES to meet a
global target of $2^{\circ}$C rise by 2050 is paramount[1, 2, 3, 4, 5, 6, 7,
8, 9]. Graphically, the Sankey diagram developed by the Lawrence Livermore
National Laboratory and shown in Fig. 1 depicts the AMES’ flow of energy from
primary fuels to four energy consuming sectors[10]. It reveals that the three
carbon-intensive fuels of natural gas, petroleum, and coal account for 80% of
the AMES’ supply side. In the meantime, 37% of American energy supply and more
importantly 100% of renewable energy supply flows through electric generation
facilities where they are then rerouted to the residential, commercial,
industrial and transportation sectors. On the demand side, 67% of all energy
consumed is lost as rejected energy. The transportation sector, in particular,
rejects $~{}80\%$ of its energy and is consequently the lead producer of
greenhouse gas (GHG) emissions[11]. To significantly reduce the GHG emissions
produced from fossil fuels, three _architectural changes_ are simultaneously
required[2]. First, carbon-neutral renewable energy sources such as solar,
wind, nuclear, geothermal and nuclear generation must be increasingly
integrated into the grid and ultimately displace fossil-fuel fired generation
plants; especially as they are retired at the end of their useful life[12, 13,
14, 9, 15, 16]. Second, energy consumption technologies, like transportation
and heating, that rely heavily on fossil-fuel combustion must switch fuels to
electricity where they have opportunity to be powered by an increasingly
decarbonized electric power. Lastly, energy-intensive technologies throughout
the AMES must be systematically replaced with their more energy-efficient
counterparts[17, 18, 19, 20, 21, 22].

Together, these three architectural changes minimize the demand on the coal,
oil, and natural gas systems. In the meantime, such a systemic shift towards
the use of electricity requires a commensurate expansion of the electric grid.
Such a _sustainable energy transition_ is arguably the largest single
engineering system transformation in human history. Given the environmental
consequences, it must be undertaken in a manner that not just meets the
evolving requirements of its stakeholders but also in the meantime remains
operational. Fortunately, from a model-based systems engineering perspective,
the three architectural changes described above constitute a change in the
AMES’ _instantiated architecture_ but leaves the AMES’ _reference
architecture_ largely unchanged. For this reason, identifying the underlying
reference architecture of the AMES becomes a high priority in meeting the
paramount requirement of energy sustainability.

######  Definition 1.

\- Instantiated Architecture A case specific architecture, which represents a
real-world scenario, or an example test case. At this level, the physical
architecture consists of a set of instantiated resources, and the functional
architecture consists of a set of instantiated system processes. The mapping
defines which resources perform what processes.

######  Definition 2.

\- Reference Architecture[23] “The reference architecture captures the essence
of existing architectures, and the vision of future needs and evolution to
provide guidance to assist in developing new instantiated system
architectures. …Such reference architecture facilitates a shared understanding
across multiple products, organizations, or disciplines about the current
architecture and the vision on the future direction. A reference architecture
is based on concepts proven in practice. Most often preceding architectures
are mined for these proven concepts. For architecture renovation and
innovation validation and proof can be based on reference implementations and
prototyping. In conclusion, the reference architecture generalizes
instantiated system architectures to define an architecture that is generally
applicable in a discipline. The reference architecture does however not
generalize beyond its discipline.”

Figure 1: A Sankey Diagram of U.S. Energy Consumption in 2019. The Lawrence
Livermore National Laboratory has produced this visualization based primary
data sources from the DOE and EIA[10].

From a resilience and reliability perspective, each of the AMES’ component
systems must not just deliver their respective type of energy independently[1,
24, 25, 26, 27] but must also support the other AMES infrastructures as
well[28]. For example, and as shown in Fig. 1, if a natural gas pipeline fails
in the natural gas system it could take a natural gas power plant offline in
the electric grid. Such a lack of electric generation capacity could then
result in the temporary shut down of a natural gas processing plant; further
reducing natural gas and electricity capacity. The New England electric power
grid, in particular, remains susceptible to natural gas shortages during long
cold spells when the fuel is used heavily for both space heating as well as
electric generation[29]. Alternatively, the oil and natural gas systems rely
on electricity to process their respective fuels and compress them during
storage and transportation. Even the coal system requires electricity in safe
and efficient mining.

As the AMES’ architecture evolves through the sustainable energy transition,
it must do so in a manner that is reliable and resilient to natural, economic
and malicious disruptions. By modeling and understanding the instantiated
architecture of the AMES at each stage of this sustainable energy transition,
system-wide vulnerabilities can be systematically identified and mitigated in
a way that is more comprehensive than if each infrastructure were studied
independently. For example, global climate change and severe weather events
may place coastal energy facilities particularly at risk[30]. In the meantime,
economic shocks can affect the import and export energy resources and disrupt
their relative balance in the AMES[31]. Finally, malicious cyber-attacks can
propagate failures not just within a given AMES infrastructure but across them
as well.

Finally, from an energy access perspective, the AMES must continue to cost-
effectively and equitably provide readily available energy to the broader
public [32]. Relative to many other nations, this requirement has been largely
addressed in the United States. Nevertheless, certain issues remain. For
example, in northern New England, people rely on carbon-intensive oil and
propane for heating. In the meantime, heat pumps have limited performance in
especially cold climates. Finally, solar and wind potential is often plentiful
away from urban load centers and so may not be effectively tapped without
additional electric transmission capacity[33, 34, 35, 36, 37, 38, 39, 40].
Many of these energy access concerns are particularly poignant in Alaska and
other arctic regions.

The three general requirements of energy sustainability, resilience, and
access impose constraints on the evolution of the AMES’ architecture. And yet,
the AMES’s architecture remains relatively poorly understood from a holistic
perspective[41, 42, 43, 44]. The Sankey Diagram in Fig. 1, to our knowledge,
presents the only graphical depiction of the AMES in its entirety. While this
data visualization effectively conveys information concerning relative energy
flows, from a model-based systems engineering[45] perspective, its highly
simplified nature was not intended for architectural analysis and design. In
addition to the Sankey model, the EIA has developed the National Energy
Modeling System (NEMS) software to produce the yearly annual energy
outlook[11]. Nevertheless, this software-based tool remains less than
transparent and the EIA website itself states: “[The] NEMS is only used by a
few organizations outside of the EIA. Most people who have requested NEMS in
the past have found out that it was too difficult or rigid to use [46]”.

Figure 2: The top level internal block diagram of the AMES. The domestic
supply sources, the energy imports, natural environment, domestic consumption,
energy exports, and water treatment are external to the AMES’ four subsystems
of coal, natural gas, oil, and electric grid.

###  I-A Original Contribution

This paper defines a reference architecture in a single invariant SySML model
describing the four main systems that comprise the unified AMES. The top level
block diagram in Figure 2 presents the four subsystems of the AMES and the
flow of operands between them and those entities defined as outside of the
system boundary. Each of the four subsystems: electric grid, natural gas
system, oil system, and coal system are in turn defined using block definition
and activity diagrams with (allocation) swim-lanes. Integrating each of the
sub-reference architecture block definition and activity diagrams as described
in the AMES block diagram defines the entirety of the AMES reference
architecture. This work assumes a working knowledge of the SysML (the Systems
Modeling Language) which is otherwise gained from several excellent texts[45,
47, 48].

###  I-B Paper Outline

Section II starts with a description of the background literature and the
datasets used to develop the reference architecture. The paper then presents
the electric power system’s architecture in Section III-A. The natural gas
architecture is then presented in Section III-B. The oil system and coal
system architectures are then defined in Section III-C and Section III-D
respectively. A discussion of dependencies between each of the subsystems is
presented in Section IV. The paper then presents future work of the AMES
reference architecture. This includes simulation development for integrated
planning and operations management. Finally, the paper is brought to a
conclusion in Section V.

##  II Background

Normally, each of the four systems of the AMES are studied independently and
each have their own extensive literature[49, 50, 51, 52]. Increasingly,
however, sustainability, resilience, and accessibility drivers have brought
about greater attention to how these individual infrastructures depend on each
other[53, 54, 55, 56, 57]. One dependence that has received considerable
attention is the dependence of the electric grid on the natural gas system
[58, 59, 29, 60, 61, 62, 63]. These works are motivated by the increasing role
of natural gas-fired electricity generation relative to coal-fired
facilities[64], and the importance of natural gas power plants in providing
“flexible” operating reserves against variable renewable energy resources[65].
Similarly, some works have addressed the dependence of the electric grid on
the oil[51, 66] and coal systems [67, 52]. Moving beyond the specific scope of
the AMES, a related but extensive literature has developed on the co-
dependence of the electric grid and water resources in the form of the Energy
Water Nexus (EWN) [68, 69, 70, 71, 72, 73, 74, 75, 76, 15, 77, 78, 79, 80,
81]. Together, these works provide an insight into the structural and
behavioral complexity of the AMES. Furthermore, they also demonstrate the
potential benefits of analyzing and optimizing the AMES as a single system-of-
systems rather than each system independently[82].

It is worth mentioning that much of these works focus on a single interaction
between two energy systems and consequently, to our knowledge, this is the
first work to address the architecture of the AMES as a whole. Furthermore,
because the focus is usually on a single interaction, there has been little
effort[68, 83, 84] to deploy a model-based systems engineering methodology
where a system boundary is rigorously defined and then later elaborated in
terms of physical interfaces and functional interactions. Ultimately, a
complete architectural description is necessary to ensure that 1.) energy and
mass conservation laws are respected, 2.) all environmental aspects are
identified in environmental impact assessments[85], and 3.) the greatest
potential for synergistic outcomes are found. Finally, the use of model-based
systems engineering modeling conventions (such as SysML) maximizes the
potential for cross-disciplinary communication and coordination.

This paper uses the S&P Global Platts (GIS) map data pro data set[86] and the
EIA Annual Energy Outlook dataset [11] to deduce the AMES’ reference
architecture. Both datasets are labeled with metadata that correspond to
classes and attributes in the AMES’ form. The classes and their associated
behaviors are shown here, but their attributes have been suppressed for
brevity. The interested reader is referred to original references for
attribute metadata. Next, each GIS layer of the Platts dataset includes
descriptions of facility types and their associated products. This data can be
used to deduce the associated function(s) of these facilities. Finally, the
process technologies for all of the AMES’ constitutent energy facilites are
well known. Therefore, this work relies on engineering textbook knowledge of
these facilities to supplement the Platts and EIA datasets with low-level
knowlege of input-output interfaces. Lastly, because Platts and EIA datasets
only include bulk, wholesale, and transmission level assets of conventional
energy technoloiges, this paper is similarly limited in its scope.

##  III Modeling

This paper uses the Systems Modeling Language (SysML)[47, 87, 88, 48, 89, 45,
90] to define the AMES reference architecture. Fig. 2 shows the system
boundary of the AMES around its four constituent energy systems of
electricity, oil, natural gas and coal. The high level flows of matter and
energy between these four energy systems and across the system boundary are
also defined. The matter and energy flows in Fig. 2 also restrict the set of
operands in the AMES. While the Platts dataset does specify a much larger
number of energy products, this analysis, for tractability, has classified all
flows of matter and energy into the following set of operands: coal, raw
natural gas, processed natural gas, crude oil, processed oil, syngas, liquid
biomass feedstock, solid biomass feedstock, solar irradiance, wind energy,
uranium, water energy (for cooling), electric power, withdrawn water, mine
effluent, processing effluent, and thermal effluent.

Figure 3: AMES block definition diagram showing its four component systems.

From a form perspective, Fig. 3 presents a block definition diagram of the
AMES and its four constituent energy systems as classes. For graphical
simplicity, each of these energy system classes adopt attributes to represent
their component infrastructure facilities and resources. Furthermore,
association links are removed for graphical clarity and may be otherwise
deduced from the associated activity diagram. The following subsections
elaborate the form and function of these systems in turn.

###  III-A Electric Power System

The Electric Power System is comprised of resources for the generation,
transmission, and routing of electric power. Power plants comprise a majority
of the different types of resources within the electric grid. Each power plant
type is designated by the primary fuel category used to generate electric
power. There are thus nine different types of power plants present: coal,
natural gas, syngas, oil, biomass, nuclear, solar, hydro, and wind. These
power plants are connected to the electric grid by transmission lines (to the
distribution system). The last component of the electric grid that realizes
the end of the electric grid value chain is substations where the electric
power leaves the transmission system. Fig. 4 presents the formal decomposition
of the AMES electric grid architecture.

Figure 4: Electric grid block definition diagram showing its component
physical resources.

Each of the individual resources within the electric power system have their
respective processes. Fig 5 presents the electric grid activity diagram that
shows these processes allocated onto their respective form in swim-lanes and
follows the flows of matter and energy between the processes. Each power plant
has their respective generate electric power process from their designated
fuel source. The thermal generation processes Generate Electricity from Coal,
Generate Electricity from Processed NG, Generate Electricity from Syngas,
Generate Electricity from Processed Oil, Generate Electricity from Liquid
Biomass, Generate Electricity from Solid Biomass, and Generate Electricity
from Uranium each take their respective fuel source and withdrawn water as
inputs and result in electric power, thermal losses, power plant thermal
effluent, and power plant thermal evaporation. Aside from electric power, all
of the remaining outputs immediately leave the system boundary. In contrast,
the electric power is then transported by the transmission lines. The electric
grid value chain is completed at the substation which routes the electric
power to the other AMES energy systems or to the electric distribution system
outside the scope of this reference architecture.

Figure 5: Electric grid activity diagram with allocated swim lanes.

###  III-B Natural Gas System

The natural gas system is comprised of resources for the import, export,
processing and delivery of natural gas. The Receipt Delivery and LNG Terminals
are responsible for importing and exporting natural gas into and out of the
natural gas system. These resources take both international and domestic
imports into the United States’ natural gas pipeline infrastructure. Pipelines
and compressors are present for facilitating the transportation of natural
gas. Additionally, Processing plants are present for processing raw natural
gas. Finally, storage facilities store syngas as well as raw and processed
natural gas. Fig. 6 presents the formal decomposition of the AMES’s natural
gas system architecture.

Figure 6: Natural Gas system block definition diagram showing its component
physical resources.

Each of the individual resources within the natural gas system have their
respective processes. Fig. 8 presents the natural gas activity diagram. It
shows natural gas processes allocated onto their respective form in swim-lanes
and follows their flow of matter and energy. The Receipt Delivery facility can
import and store syngas, raw natural gas, and processed natural gas as well as
export the processed natural gas out of the system boundary. The LNG Terminal
can import, store and export natural gas. Once inside the natural gas system,
pipelines transport each of the operands, syngas, raw natural gas and
processed natural gas, through the United States. This includes pipelines that
transport directly to natural gas electric power plants in the electric grid.
With the inputs of raw natural gas, electric power and withdrawn water,
processing plants process raw natural gas to produce processed natural gas and
processing effluent. Compressors stimulate the transportation of the different
types of natural gas by adjusting the associated pressure. Finally, storage
facilities store syngas as well as raw and processed natural gas.

###  III-C Oil System

The oil System is comprised of resources for the import, export, and delivery
of oil. The Oil Port and oil Terminal are responsible for importing and
exporting oil into and out of the oil system. These resources take both
international and domestic imports into the United States’ oil pipeline
infrastructure. Crude and processed oil pipelines are present for facilitating
the transportation of oil and liquid biomass. Oil Refineries allow for the
processing of crude oil into processed oil, and oil buffers allow for storage
within the oil system infrastructure. Fig. 7 presents the formal decomposition
of the AMES’s oil system architecture.

Figure 7: Oil system block definition diagram showing its component physical
resources. Figure 8: Natural gas system activity diagram with allocated swim
lanes. Figure 9: Oil system activity diagram with allocated swim lanes. Figure
10: Coal system activity diagram with allocated swim lanes.

Each of the individual resources within the oil system have their respective
processes. Fig. 9 presents the oil activity diagram. It shows the oil system’s
processes allocated onto their respective form in swim-lanes and follows their
flows of matter and energy. The Oil Terminal facility can import and export
crude oil, processed oil and liquid biomass to and from outside the system
boundary. The Oil Port can also import and export crude and processed oil.
Once inside the oil system, the crude oil pipeline can transport crude oil
from an oil port or terminal to an oil refinery where the crude oil is
processed into processed oil. This process requires the input of crude oil,
electricity and withdrawn water to produce processed oil, syngas[91] and
processing effluent. The processed oil can then be transported by the
processed oil pipelines. These processed oil pipelines transport processed oil
and liquid biomass within the oil system and directly to oil and liquid
biomass electric power plants in the electric grid. Additionally, all three
operands, crude oil, processed oil, and syngas can be stored within the oil
system by oil buffers.

###  III-D Coal System

The coal System is comprised of resources for the import, export, and delivery
of coal. The coal sources are responsible for mining domestic sources of coal
and introducing coal into the United states coal system. Coal docks are also
responsible for the import and export of coal. Rail roads are responsible for
transporting coal across the United states and to coal electric power plants
in the electric grid. Finally, coal buffers allow for the storage of coal
within the system boundary. Fig. 11 presents the formal decomposition of the
AMES’s coal system architecture.

Figure 11: Coal system block definition diagram showing its component physical
resources.

Each of the individual resources within the coal system have their respective
processes. Fig 10 presents the oil activity diagram. It shows these processes
allocated onto their respective form in swim-lanes and follows their flow of
matter and energy. With the input of electric power and withdrawn water, the
coal source can mine coal to produce coal and mine effluent. Alternatively,
the coal docks can import coal into the coal system which can then be
transported by the rail roads. The coal can then be stored within a coal
buffer or exported out of the coal system boundary by a coal dock.

##  IV Discussion

The activity diagrams in Figs. 5, 8, 9, 10 each show the individual energy
systems that when integrated together form the AMES shown in Fig. 2. When
following the flows of matter and energy through the AMES, it becomes apparent
that every subsystem is connected to the other. The coal system produces and
imports coal that is delivered to the electric grid for electric power
generation. The oil system is able to produce and deliver syngas to the
natural gas system as well as deliver processed oil and liquid biomass to the
electric grid for electric power generation. The natural gas system is able to
deliver syngas and processed natural gas to the electric grid for electric
power generation. Finally, the electric grid is able to deliver electric power
to the coal system for mining, the oil system for processing crude oil, and to
the natural gas system for processing raw natural gas and gas compression.
Each of these connections allow the electric grid to produce electric power
from the other energy systems’ fuel sources and subsequently deliver power to
the United states. Additionally, the electric power allows for the production
and processing of operands in the coal, oil, and natural gas systems so that
they may provide fuel sources back to the electric grid and the rest of the
United States’ fuel demands.

Understanding the nature of such interdependencies within the AMES’ reference
architecture facilitates changes to the AMES as it is currently instantiated
architecture[92, 93, 94]. This knowledge becomes particularly important in
avoiding cross-sectoral cascading failures [54, 95, 25]. For example, if a
natural gas pipeline fails there is not only a loss of natural gas being
delivered for heating but for electric power generation as well. Unavailable
electric power plants not only diminishes the grid’s ability to meet
residential, commercial, and industrial demand but also the load demanded by
the other energy systems.

These interdependencies in the AMES’ reference architecture often exaggerate
“infrastructure lock-in” effects that impede the forward-motion of the
sustainable energy transition[96, 97, 98, 99]. As coal power plants are
decommissioned, natural gas power plants are often installed in their place
with commensurate reductions in greenhouse gas emissions. These benefits,
however, are not realized until sufficient natural gas pipeline capacity is
secured; either on existing or potentially new pipelines. Similarly, electric
power transmission capacity often impedes the full utilization of remote solar
and wind generation resources. Alternatively, the presence of excess
processing and transmission capacity for coal, oil, and natural gas makes it
very easy and economical to rely on these sources in the electric power
sector. For example, the electric power grid is likely to retain its reliance
on the natural gas system for a long time because so much of the country
relies on natural gas for heating. In short, an effective “deep”
decarbonization strategy requires the coordination of all four energy sectors
and not just one alone.

###  IV-A Simulation Model Development

The development of the AMES reference architecture facilitates the subsequent
development of mathematical models and simulations of system behavior. As a
relevant precedent, the energy-water nexus reference architecture[68, 83] led
to the development of holistic mathematical models[73, 100, 71, 72, 70] which
were later implemented as numerical simulations. To this end, the reference
architecture provides the starting point for a _transparent_ objected-oriented
software design grounded in “digital twin” principles. Much like the National
Energy Modeling System (NEMS)[101], the AMES reference architecture can be
used to model and simulate the effect of potential policies and future
infrastructure developments. By changing the ratios of instantiated
technologies, different scenarios can be analyzed and outcomes compared. For
example, the energy-water nexus mathematical models were later used to conduct
sensitivity analyses and identify input/output trade-offs[74, 76, 73, 75, 84].
The AMES reference architecture can also potentially import much of the openly
available socio-economic NEMS data. Finally, recent theoretical works[102,
103, 26] have shown that SysML-based reference architectures of interdependent
infrastructure systems can be translated, without loss, into mathematical
structural models called hetero-functional graphs. These hetero-functional
graphs can then be used to study the AMES’ structural resilience[103, 26] in
terms of its ability to resist cross-sectoral and cascading disruptions.

###  IV-B Integrated Planning and Operations

Just as the the AMES reference architecture allows for the simulation and
analysis of differing policies across the entirety of the AMES, it also allows
for integrated planning and operations management. By planning future
infrastructure developments with an integrated view of the whole AMES,
developments with the greatest impact can be planned and installed. This
allows for a holistic planning effort that incentivizes simultaneous
developments in multiple energy systems such that they compliment rather than
impede each other. For example if a coal mine is decommissioned in the coal
system, then a coal power plant in the electric grid could be replaced with a
less carbon-intensive power plant. The EWN literature has already demonstrated
similar benefits[104, 77, 78, 79, 74, 105]. For example, the straightforward
installation of water storage capacity has been shown to alleviate power
balance constraints in the electric power grid where the installation of
battery energy storage is at a premium. Similarly, the natural gas-electricity
literature has shown pairing natural gas electric power plants with variable
energy resources (VER) such as wind turbines provides a smaller carbon
footprint with renewable wind energy and natural gas replacing coal[106, 60,
107]. Additionally, the fast ramping capacity of natural gas power plants
provides reliability in maintaining a stable grid in the presence of VERs. In
all of these cases, one or more layers of planning and operations management
decision-making are superimposed on the mathematical model of the underlying
interdependent infrastructure system. The instantiation of the AMES reference
architecture is the first step to joint optimization and operation of these
four energy systems.

##  V Conclusion

The American Multi-modal Energy System reference architecture is an invariant
reference architecture that describes the electric grid, oil system, natural
gas system, and coal system as well as their inter-dependencies. As American
energy demands in the 21st evolve to meet new requirements for energy
sustainability, resilience, and access, the AMES’ instantiated architecture
will also evolve, but the AMES’ reference architecture will remain largely
unchanged. Instead, the ratios of instantiated elements will change resulting
in more carbon-intense resources being instantiated less and carbon-lite or
carbon-free resources being instantiated more. The AMES reference architecture
provides the basis from which to run simulations on new policies and the
associated changes of instantiated architecture. Furthermore, the AMES
reference architecture facilitates the formulation of new optimal planning and
operations management decisions. As previously demonstrated in the NG-
Electricity nexus literature and the energy-water nexus literature, these
decisions can identify synergistic strategies that simultaneously enhance
infrastructure cost, reliability and sustainability. Such synergistic
strategies are often able to overcome typical “infrastructure lock-in”
scenarios and the ensuing “trilemma” debates on energy sustainability,
resilience, and access. In short, holistic models AMES models present new
possibilities for energy infrastructure coordination that may have been
otherwise overlooked when addressing each energy infrastructure independently.

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|  Dakota J. Thompson graduated from Colby College in 2018 with a B.A. in
Physics and minor in Computer Science. He is now pursuing a Ph.D. in energy
systems engineering at the Thayer School of Engineering at Dartmouth. As an
undergraduate, Dakota worked on several reseearch projects with the LIINES at
the Thayer School of Engineering at Dartmouth and continues his research in
power grid resilience, renewable energy integration, and hetero-functional
graph theory.
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|  Amro M. Farid is currently an Associate Professor of Engineering at the
Thayer School of Engineering at Dartmouth and Adjunct Associate Professor of
computer science at the Department of Computer Science. He leads the
Laboratory for Intelligent Integrated Networks of Engineering Systems
(LIINES). The laboratory maintains an active research program in Smart Power
Grids, Energy-Water Nexus, Energy-Transportation Nexus, Industrial Energy
Management, and Integrated Smart City Infrastructures. He received his Sc. B.
in 2000 and his Sc. M. 2002 in mechanical engineering from MIT and his Ph.D.
degree in Engineering from the U. of Cambridge (UK).
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