As a D i e: Pa icle-based P opulsion
Sys em
Jae Un Kim
Depa men o Physics, Ajou Uni e si y, Republic o Ko ea
[email p o ec ed]
Abs ac
Con en ional p opulsion sys ems a e undamen ally cons ained by he Tsiolko sky
ocke equa ion, which equi es exponen ial p opellan mass g ow h o achie e high
e minal speeds. E en ad anced elec ic p opulsion and ion h us e s, while highly
e icien , emain limi ed by mass a ios and onboa d p opellan s o age.
This wo k de elops a ull heo e ical o mula ion o he As a D i e, a nea – u u e
ela i is ic pa icle–packe p opulsion sys em in which mul iple compac pa icle accel-
e a o s moun ed on he ea o a spacec a con inuously ejec ela i is ic ion packe s
(o p o on packe s), gaining momen um om con inuous eac ion.
The ene gy sou ce is assumed o be a high-powe nea – u u e-gene a ion sys em
in he ew-hund ed-megawa class. This decouples h us gene a ion om chemical
p opellan mass and emo es he Tsiolko sky cons ain .
We p esen : (i) a ela i is ic momen um– h us amewo k, (ii) packe ized emission
dynamics a MHz– ens-o -MHz epe i ion a es, (iii) a quan i a i e h us model using
nea - u u e achie able pa icle accele a o powe (80 MW pe uni , 5 uni s, P o =
400 MW), (i ) long-du a ion pe o mance o a 5-uni pa icle accele a o con igu a ion
( he numbe o uni s is no ixed), ( ) mission-scale p edic ions showing ha a eloci y
inc emen o ∆ ∼8.4×104m/s (abou 84 km/s, 2.8×10−4c) is eachable wi hin one
yea o con inuous ope a ion o an 800 kg spacec a .
We emphasize ha he pa icle species (p o ons o Helium ion) and pa icle ac-
cele a o pa ame e s a e placeholde s and can be modi ied in u u e implemen a ions.
(The pe o mance alues p esen ed in his s udy co espond o a conse a i e base-
line con igu a ion o 400 MW o elec ical powe and an 800 kg spacec a mass. Any
inc ease in a ailable powe o u he s uc u al mass educ ion would p opo ionally
enhance he achie able wi hin he same p opulsion amewo k.)
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1 In oduc ion
Achie ing high spacec a eloci ies emains one o he g and enginee ing obs acles o mode n
as ophysics. Chemical ocke s a e undamen ally cons ained by he Tsiolko sky ocke
equa ion:
∆ = eln m0
m ,(1)
whe e eis exhaus eloci y and m0/m is he mass a io. Ion p opulsion sys ems inc ease
ebu a e s ill bound o ca ying p opellan .
A p opulsion sys em ha emo es he onboa d p opellan equi emen would undamen-
ally bypass hese limi s. The As a D i e p oposes such a sys em: ejec ing high– eloci y
pa icle packe s p oduced by compac pa icle accele a o s a he han s o ed uel.
1.1 Concep ual Mo i a ion
The As a D i e is based on ou obse a ions:
1. Rela i is ic pa icles (p o ons o ions) can be accele a ed e icien ly using compac
RF/lase hyb id pa icle accele a o s.
2. Momen um ans e om a con inuous packe s eam can p oduce sus ained h us
independen o chemical p opellan .
3. Nea - u u e usion o high-densi y powe sys ems may p o ide elec ical powe in he
O(102) MW ange.
4. Long-du a ion accele a ion (mon hs o yea s) allows cumula i e speed g ow h o he wise
impossible.
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2 Ope a ing P inciple
The As a D i e gene a es h us by expelling ul a- ela i is ic pa icle packe s p oduced by
a compac pa icle accele a o ins alled a he ea sec ion o he spacec a . Unlike chemical
ocke s, he sys em does no ely on p opellan mass ca ied in la ge quan i ies. Ins ead, a
small onboa d supply o pa icles is epea edly accele a ed o nea -ligh -speed eloci ies and
ejec ed di ec ionally, p oducing momen um ans e acco ding o ela i is ic conse a ion
laws.
2.1 Pa icle Injec ion and Accele a ion
A small ese oi o cha ged pa icles (p o ons o ligh ions) is injec ed in o a compac
pa icle accele a o . The accele a o employs hyb id RF–lase ields o p oduce con inuous
mic o-bunching and high-g adien accele a ion. Each pa icle packe achie es eloci ies in
he ange:
p= 0.90c,
depending on he a ailable onboa d powe and accele a o e iciency.
The packe p oduc ion a e is deno ed by R(packe s pe second). A nea - u u e ealis ic
achie able ange in compac accele a o s lies in he MHz egime:
R∼107packe s/s.
In he pe o mance es ima es below, he h us is exp essed in e ms o o al accele a o
powe , so he de ailed choice o Rand pa icles pe packe is abso bed in o he powe budge .
A key cha ac e is ic o he As a D i e is ha i s achie able eloci y inc eases app oxi-
ma ely linea ly wi h a ailable elec ical powe . Unlike chemical o elec ic p opulsion sys ems
cons ained by p opellan mass a ios, he As a D i e’s momen um- ans e mechanism
scales di ec ly wi h inpu powe . The e o e, highe powe a ailabili y (e.g., mul i-GW-class
u u e sys ems) would p opo ionally inc ease con inuous h us and allow eloci y egimes
a beyond he 84 km/s demons a ed in he nea - u u e 400 MW e e ence con igu a ion.
2.2 Rela i is ic Momen um Ejec ion
Each accele a ed packe has ela i is ic momen um:
pp=γmp p, γ =1
p1−( p/c)2,
whe e mpis he pa icle mass.
As he packe exi s he nozzle in a collima ed beam, he eac ion gene a es h us :
F=R pp.
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2.3 Con inuous Th us Buildup
Because he As a D i e does no consume p opellan mass in he con en ional sense, h us
can be applied o mon hs o yea s. The spacec a mass Ms emains nea ly cons an ,
enabling long-du a ion accele a ion:
a( ) = F
Ms
.
E en a small h us accumula ed o e long du a ions esul s in signi ican eloci y g ow h:
( ) = Z
0
a(τ)dτ.
2.4 Long-Du a ion Rela i is ic C uise
Fo a spacec a o mass Ms= 800 kg and a o al accele a o powe supply o P o = 400 MW
(5 uni s ×80 MW), he As a D i e can each, unde cons an - h us app oxima ion:
1 mon h ≈7×103m/s ≈7 km/s,
1 yea ≈8.4×104m/s ≈84 km/s ≈2.8×10−4c.
These eloci ies al eady exceed ypical chemical escape eloci ies and a e ob ained wi h-
ou he exponen ial uel penal y o chemical o ion engines, while emaining wi hin a high
bu concei able nea - u u e powe budge .
2.5 Key Ad an age: Escape F om he Rocke Equa ion
The As a D i e ci cum en s he adi ional Tsiolko sky ocke equa ion because h us
comes om accele a ing a iny mass epea edly ins ead o ejec ing la ge p opellan mass:
∆ As a ∝ , ∆ ocke ∝ln(m0/m ).
Thus, he sys em p o ides sus ained, scalable, and long-du a ion ela i is ic accele a ion
una ainable wi h cu en chemical p opulsion me hods.
3 Rela i is ic Momen um–Th us Fo malism
A packe o mass mpemi ed a ela i is ic eloci y phas momen um
pp=γmp p,(2)
whe e
γ=1
q1− 2
p/c2
.(3)
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I packe s a e emi ed a equency (packe s/s), he a e age h us is
F= γmp p.(4)
O e du a ion T:
∆ =F
Ms
T, (5)
whe e Msis spacec a mass.
3.1 Powe Cons ain
Accele a ing one packe o kine ic ene gy
Ek= (γ−1)mpc2(6)
equi es beam powe
P= Ek= (γ−1)mpc2.(7)
Fo ixed pa icle accele a o powe Pacc, we ob ain
=Pacc
(γ−1)mpc2.(8)
Subs i u ing in o F:
F=Pacc
c2
γ p
(γ−1).(9)
This p o ides a closed- o m h us exp ession de e mined solely by powe and exhaus
eloci y, and is he basis o he nume ical es ima es below.
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4 Sys em A chi ec u e
4.1 Choice o Pa icle Species
In his pape we conside wo easible pa icle species o nea – u u e mic o-accele a o
p opulsion:
Species: Helium ion (He+/ He2+)
•Jus i ica ion:
–mode a e cha ge- o-mass a io
–highe momen um pe ion packe a ela i is ic eloci y
– educed beam di e gence due o la ge mass
–s able accele a ion in hyb id RF/lase mic o-accele a o s
–Helium ions a e compa ible wi h exis ing lase –wake ield and RF accele a ion
expe imen s, enabling nea - e m expe imen al alida ion.
•Helium ions may ope a e in mixed-ion mode wi h p o ons o op imize h us , beam
s abili y, and ene gy e iciency.
Species: P o on (p+)
•Jus i ica ion:
–high cha ge- o-mass a io
–s able accele a ion
– ich expe imen al da a
–compa ible wi h RF/lase hyb id mic o-pa icle accele a o s
•Fu u e implemen a ions may subs i u e elec ons, muons, deu e ons, o mixed packe s.
4.2 Pa icle Accele a o s Con igu a ion
We assume:
N= 5, Puni = 80 MW, P o = 400 MW.
This lies wi hin a high bu concep ually nea - u u e easibili y window based on ad anced
usion-elec ic o supe conduc ing powe sys ems.
4.3 Emission Veloci y
We adop :
p= 0.90c
which co esponds o:
γ= 2.29.
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5 Pe o mance Es ima ion
5.1 Th us Calcula ion
Using he powe -limi ed h us o mula:
F=P o
c2
γ p
(γ−1).
Fo p= 0.9c,γ= 2.29 and P o = 400 ×106W:
γ p
(γ−1)c2=2.29 ×0.9c
1.29 c2≈5.32 ×10−9s/m.
Thus,
F≈400 ×106×5.32 ×10−9N≈2.1 N.
5.2 Accele a ion
Fo a spacec a mass Ms= 800 kg:
a=F
Ms
≈2.1
800 m/s2≈2.6×10−3m/s2.
5.3 Veloci y a e One Yea
Wi h T= 3.15 ×107s:
∆ =aT ≈2.66 ×10−3m/s2×3.15 ×107s≈8.4×104m/s = 83.9 km/s ≈2.8×10−4c.
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6 Feasibili y o Nea -Te m Implemen a ion
The As a D i e elies on ela i is ic pa icle exhaus gene a ed by compac pa icle accel-
e a o s. Unlike la ge e es ial accele a o acili ies, ecen ad ances allow high-g adien
pa icle accele a ion wi hin me e -scale o e en sub–me e -scale a chi ec u es. The e o e,
he sys em does no equi e any new physics beyond es ablished accele a o and plasma
science, bu i does assume high-densi y powe sys ems in he ew-hund ed-megawa class.
6.1 Compac Pa icle Accele a o Technologies
Th ee expe imen ally e i ied accele a o pla o ms suppo he nea - e m easibili y o he
As a D i e:
1. RF Mic o Pa icle Accele a o s: Mode n RF-d i en pa icle accele a o ca i ies
achie e accele a ing g adien s o 20–50 MV/m in s uc u es sho e han 50 cm. These
compac pa icle accele a o s can gene a e p o on o ion packe s wi h con olled kine ic
ene gy sui able o momen um- ans e p opulsion.
2. Dielec ic Lase Pa icle Accele a ion (DLA): Chip-scale pa icle accele a o
s uc u es using dielec ic lase accele a ion ha e demons a ed g adien s exceeding
300 MV/m. Al hough cu en demons a ions use elec ons, he e i ied physical mech-
anism shows ha compac , high-g adien pa icle accele a ion is expe imen ally easible
and apidly ad ancing.
3. Hyb id RF–Lase Pa icle Accele a o s: Se e al expe imen al p og ams combine
RF p e-accele a ion wi h lase - ield pos -accele a ion o enable high epe i ion a es o
pa icle packe s in he kHz–MHz ange. These epe i ion a es di ec ly ma ch As a
D i e’s con inuous packe exhaus p opulsion model when scaled o highe a e age
powe .
6.2 Ene gy Requi emen s
Conside ing a ealis ic beam and con e sion e iciency, a sys em o i e compac pa icle
accele a o s ope a ing a a combined elec ical inpu o o de
P o ≃400 MW
can gene a e a sus ained h us o a ew new ons, su icien o accumula e a measu able
∆ ∼102km/s o e a one–yea imescale. This equi emen is abo e p esen spacec a
powe le els bu wi hin he ealm o ad anced usion-elec ic o la ge-scale nuclea sys ems.
6.3 Mass and S uc u al Conside a ions
A spacec a mass o Ms≈800 kg is consis en wi h a small bu powe -dense pla o m
including powe sou ce, he mal con ol and accele a o modules. The s uc u al in eg a ion
o se e al compac pa icle accele a o s (<1 m each) is easible, and he eac ion o ces
gene a ed by he pa icle packe exhaus emain below he mechanical s esses encoun e ed
in exis ing high-powe elec ic p opulsion sys ems.
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6.4 Powe Sou ce Speci ica ion
The o al powe equi emen o 400 MW can be supplied by a compac ou h-gene a ion
nuclea ission eac o (ad anced SMR class) ope a ing in con inuous mode. Mode n high-
empe a u e gas-cooled and sodium-cooled as eac o designs al eady achie e powe den-
si ies sui able o megawa - o- gigawa elec ic ou pu in sub-10- on con igu a ions. A
space-quali ied SMR module would he e o e p o ide he equi ed elec ical powe o he
mul i-uni accele a o sys em wi hou in oking specula i e physics o a - u u e echnologies.
6.5 Summa y o Feasibili y
The As a D i e uses only es ablished physics and le e ages apid ad ances in compac
pa icle accele a o echnology. As soon as high- epe i ion, high-a e age-powe pa icle ac-
cele a o modules each s able comme cial o m oge he wi h mul i-hund ed-megawa space
powe sys ems, he As a D i e becomes a p ac ically deployable nea - e m p opulsion a -
chi ec u e. he analysis he e is in ended as a o wa d-model applicable o ad anced u u e
spacec a a chi ec u es.
7 Discussion
7.1 Scien i ic Implica ions
The As a D i e p o ides:
1. A p opulsion me hod independen o la ge ca ied p opellan mass.
2. A pa h o ∼102km/s-class c uise speeds unde con inuous mul i-hund ed-megawa
powe .
3. A scalable a chi ec u e whe e pe o mance g ows app oxima ely linea ly wi h a ailable
powe and mission du a ion.
7.2 Enginee ing Cons ain s
Key challenges include:
•was e-hea dissipa ion om high-powe pa icle accele a o s
• adia ion shielding
•beam di e gence minimiza ion
•long- e m pa icle accele a o s abili y and alignmen
Despi e hese, no undamen al physics ba ie p e en s he sys em om ope a ing in he
egime analyzed he e.
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