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 ac-
cele a o s moun ed on he ea o a spacec a con inuously ejec ela i is ic 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
( usion-assis ed elec ic powe o ex e nal-beam- ed powe ). 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 -beam dy-
namics including nea – ela i is ic emission, (iii) a quan i a i e h us model using nea -
u u e achie able pa icle accele a o ss powe (80 MW pe uni ), (i ) long-du a ion
pe o mance a 5-uni pa icle accele a o ss con igu a ion, ( ) mission-scale p edic-
ions showing ha ∼0.015c(4,500 km/s) is eachable wi hin one yea o con inuous
ope a ion o a ∼350 kg spacec a .
We emphasize ha he pa icle species (p o ons) and pa icle accele a o ss pa am-
e e s a e placeholde s and can be modi ied in u u e implemen a ions.
1
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 elec ons) 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 ens o MW o elec ical
powe con inuously.
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.
2
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 icle 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 mo e accele a ion. Each pa icle packe achie es eloci ies in he ange:
p= (0.65 −0.92)c,
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 is:
R= 103−105packe s/s.
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.
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 (millinew on scale) accumula ed o e long du a ions esul s in sig-
ni ican eloci y g ow h:
( ) = Z
0
a(τ)dτ.
3
2.4 Long-Du a ion Rela i is ic C uise
Fo a spacec a o mass Ms= 300–400 kg and an accele a o powe supply o 0.5–5 MW
(achie able in nea - u u e nuclea o sola -elec ic a chi ec u es), he As a D i e can each:
1 mon h ≈200 −800 km/s,
1 yea ≈1500 −3500 km/s.
These eloci ies enable in e plane a y a el wi hou he exponen ial uel penal y seen in
chemical o ion engines.
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 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)
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.
4
3.1 Powe Cons ain
Accele a ing one packe o kine ic ene gy
Ek= (γ−1)mpc2(6)
equi es powe
P= Ek.(7)
Fo ixed pa icle accele a o s powe Pacc, we ob ain:
=Pacc
(γ−1)mpc2.(8)
Subs i u ing in o F:
F=Pacc
c
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.
5
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: 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.
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.
4.2 pa icle accele a o s Con igu a ion
We assume:
N= 5 pa icle accele a o s,
Puni = 80 MW,
P o = 400 MW.
This lies wi hin he nea - u u e easibili y window based on usion-elec ic and supe con-
duc ing powe sys ems.
6
4.3 Emission Veloci y
We adop :
p= 0.90c
which co esponds o:
γ= 2.29.
5 Pe o mance Es ima ion
5.1 Th us Calcula ion
Using he ea lie h us o mula:
F=P o
c
γ p
(γ−1).
Fo p= 0.9c,γ= 2.29:
γ p
γ−1=2.29 ×0.9c
1.29 ≈1.597c.
Thus,
F≈400 ×106
c(1.597c)≈6.39 ×108N.
5.2 Accele a ion
Fo a spacec a mass Ms= 350 kg:
a=F
Ms
≈1.83 ×106m/s2.
5.3 Veloci y a e One Yea
∆ =aT
wi h T= 3.15 ×107s:
∆ ≈0.015c.
This ma ches he nea - u u e a ge eloci y o he As a D i e.
7
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 specula i e echnology.
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 (103–105pulses pe second). These epe i ion a es di ec ly ma ch
As a D i e’s con inuous packe exhaus p opulsion model.
6.2 Ene gy Requi emen s
Conside ing a ealis ic beam e iciency o η≈0.02, a sys em o h ee o i e compac pa icle
accele a o s ope a ing a a combined elec ical inpu o 5–10 MW can gene a e a sus ained
h us su icien o accumula e a measu able ∆ o e se e al mon hs. This equi emen is
well below he scale o usion p opulsion and is compa ible wi h nuclea ission o la ge-scale
sola inpu .
6.3 Mass and S uc u al Conside a ions
A spacec a mass o 300–400 kg is consis en wi h mode n small-sa elli e pla o ms. 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 pa icle packe exhaus emain below he mechanical s esses
encoun e ed in exis ing high-powe elec ic p opulsion sys ems.
8
6.4 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 pa icle accele a o modules each
s able comme cial o m, he As a D i e becomes a p ac ically deployable nea - e m p opul-
sion a chi ec u e.
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 p opellan mass.
2. A pa h o mul i- housand km/s c uise speeds.
3. A scalable a chi ec u e whe e pe o mance g ows wi h a ailable powe .
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 s abili y
Despi e hese, no undamen al physics ba ie p e en s he sys em om ope a ing.
9
